TRẦN MINH TƯỜNG

Khởi động trang 6 Toán 9 Tập 1: Độ cao h (mét) của một quả bóng gôn sau khi được đánh t giây được cho bởi công thức h = t(20 – 5t). Có thể tính được thời gian bay của quả bóng từ khi được đánh đến khi chạm đất không?<img alt="Khởi động trang 6 Toán 9 Tập 1 Chân trời sáng tạo | Giải Toán 9" src="https://vietjack.com/toan-9-ct/images/khoi-dong-trang-6-toan-9-tap-1.PNG" style="border: 0px; box-sizing: border-box; display: inline; margin-left: auto; margin-right: auto; max-width: 100%; padding-bottom: 4px; vertical-align: middle;" />Lời giải:Sau bài học này ta giải quyết được bài toán như sau:Trước khi quả bóng được đánh lên và khi quả bóng chạm đất thì quả bóng đều ở độ cao là h = 0.Thay h = 0 vào công thức đã cho, ta được:t(20 – 5t) = 0t = 0 hoặc 20 – 5t = 0t = 0 hoặc t = 4.Do đó, t = 0 giây là lúc quả bóng chưa được đánh lên cao, t = 4 giây là thời gian quả bóng được đánh lên và sau đó chạm đất.Vậy thời gian bay của quả bóng từ khi được đánh đến khi chạm đất là 4 giây.<p style="box-sizing: border-box; font-family: "Open Sans", Arial, sans-serif; font-weight: 400; left: 0px; letter-spacing: -1px; line-height: 28px; margin: 20px 0.2em 10px 0px; padding: 0px; position: relative; text-align: left; text-shadow: none;">1. Phương trình tíchKhám phá 1 trang 6 Toán 9 Tập 1: Cho phương trình (x + 3)(2x – 5) = 0. (1)a) Các giá trị <mi>x</mi><mo>=</mo><mo>&#x2212;</mo><mn>3,</mn><mtext>&#x2009;&#x2009;</mtext><mi>x</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−3,<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mo>−</mo><mn>3,</mn><mtext>  </mtext><mi>�</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math> có phải là nghiệm của phương trình không?b) Nếu số x0 khác −3 và khác <mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>2</mn></mfrac></math> thì x0 có phải là nghiệm của phương trình không? Tại sao?Lời giải:a) Thay x = –3 vào phương trình (1), ta có:(–3 + 3)[2 . (–3) – 5] = 0 . [2 . (–3) – 5] = 0.Thay <mi>x</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math> vào phương trình (1), ta có:<mfenced><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><mtext>&#xA0;</mtext><mo>.</mo><mtext>&#xA0;</mtext><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>&#x2212;</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mfenced><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mn>5</mn><mo>&#x2212;</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">(52+3)(2 . 52−5)=(52+3)(5−5)=0<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><mtext> </mtext><mo>.</mo><mtext> </mtext><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>−</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mfenced><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mn>5</mn><mo>−</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>Vậy các giá trị <mi>x</mi><mo>=</mo><mo>&#x2212;</mo><mn>3,</mn><mtext>&#x2009;&#x2009;</mtext><mi>x</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−3,<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mo>−</mo><mn>3,</mn><mtext>  </mtext><mi>�</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math> là nghiệm của phương trình đã cho.b)• Nếu x0 ≠ −3 thì x0 + 3 ≠ 0.• Nếu <msub><mi>x</mi><mn>0</mn></msub><mo>&#x2260;</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x0≠52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>�</mi><mn>0</mn></msub><mo>≠</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math> thì 2x0 – 5 ≠ 0.Do đó, nếu x0 ≠ −3 và x0 ≠ <mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-7-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>2</mn></mfrac></math> thì x0 + 3 ≠ 0 và 2x0 – 5 ≠ 0.Suy ra (x0 + 3)(2x0 – 5) ≠ 0.Vậy nếu số x0 khác −3 và khác <mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-8-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>2</mn></mfrac></math> thì x0 không là nghiệm của phương trình đã cho.Thực hành 1 trang 7 Toán 9 Tập 1: Giải các phương trình:a) (x – 7)(5x + 4) = 0;b) <mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#x2212;</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0.</mn></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">(2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+9)(23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−5)=0.<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mi>�</mi><mo>+</mo><mn>9</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>−</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0.</mn></math>Lời giải:a) Ta có: (x – 7)(5x + 4) = 0x – 7 = 0 hoặc 5x + 4 = 0x = 7 hoặc <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>4</mn></mrow><mn>5</mn></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−45<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>4</mn></mrow><mn>5</mn></mfrac></math>Vậy phương trình đã cho có hai nghiệm là x = 7 và <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>4</mn></mrow><mn>5</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−45<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>4</mn></mrow><mn>5</mn></mfrac></math>b) Ta có: <mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#x2212;</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">(2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+9)(23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−5)=0<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mi>�</mi><mo>+</mo><mn>9</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>−</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>2x + 9 = 0 hoặc <mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#x2212;</mo><mn>5</mn><mo>=</mo><mn>0</mn></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−5=0<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>−</mo><mn>5</mn><mo>=</mo><mn>0</mn></math>2x = –9 hoặc <mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>=</mo><mn>5</mn></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=5<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>=</mo><mn>5</mn></math><mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>9</mn></mrow><mn>2</mn></mfrac></math>" id="MathJax-Element-7-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−92<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>2</mn></mfrac></math> hoặc <mi>x</mi><mo>=</mo><mfrac><mn>15</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-8-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=152<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>15</mn><mn>2</mn></mfrac></math>Vậy phương trình đã cho có hai nghiệm là <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>9</mn></mrow><mn>2</mn></mfrac></math>" id="MathJax-Element-9-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−92<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>2</mn></mfrac></math> và <mi>x</mi><mo>=</mo><mfrac><mn>15</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-10-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=152Thực hành 2 trang 7 Toán 9 Tập 1: Giải các phương trình:a) 2x(x + 6) + 5(x + 6) = 0;b) x(3x + 5) – 6x – 10 = 0.Lời giải:a) Ta có: 2x(x + 6) + 5(x + 6) = 0(x + 6)(2x + 5) = 0x + 6 = 0 hoặc 2x + 5 = 0x = –6 hoặc <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>5</mn></mrow><mn>2</mn></mfrac></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>5</mn></mrow><mn>2</mn></mfrac></math>Vậy phương trình đã cho có hai nghiệm là x = –6 và <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>5</mn></mrow><mn>2</mn></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>5</mn></mrow><mn>2</mn></mfrac></math>b) Ta có: x(3x + 5) – 6x – 10 = 0x(3x + 5) – 2(3x + 5) = 0(3x + 5)(x – 2) = 03x + 5 = 0 hoặc x – 2 = 0<mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>5</mn></mrow><mn>3</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−53<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>5</mn></mrow><mn>3</mn></mfrac></math> hoặc x = 2.Vậy phương trình đã cho có hai nghiệm là <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>5</mn></mrow><mn>3</mn></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−53<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>5</mn></mrow><mn>3</mn></mfrac></math> và x = 2.Vận dụng 1 trang 7 Toán 9 Tập 1: Giải bài toán trong Hoạt động khởi động (trang 6).Lời giải:Trước khi quả bóng được đánh lên và khi quả bóng chạm đất thì quả bóng đều ở độ cao là h = 0.Thay h = 0 vào công thức đã cho, ta được:t(20 – 5t) = 0.t = 0 hoặc 20 – 5t = 0t = 0 hoặc t = 4.Do đó t = 0 giây là lúc quả bóng chưa được đánh lên cao, t = 4 giây là thời gian quả bóng được đánh lên và sau đó chạm đất.Vậy thời gian bay của quả bóng từ khi được đánh đến khi chạm đất là 4 giây.2. Phương trình chứa ẩn ở mẫu quy về phương trình bậc nhấtKhám phá 2 trang 7 Toán 9 Tập 1: Xét hai phương trình <mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mn>4</mn><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>(</mo><mn>1</mn><mo>)</mo></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2−4=1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2(1)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math class="wrs_chemistry" xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>�</mi><mo>+</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mn>4</mn><mo>=</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>(</mo><mn>1</mn><mo>)</mo></math> và 2x – 4 = 0 (2).a) Có thể biến đổi như thế nào để chuyển phương trình (1) về phương trình (2)?b) x = 2 có là nghiệm của phương trình (2) không? Tại sao?c) x = 2 có là nghiệm của phương trình (1) không? Tại sao?Lời giải:a) Trừ hai vế của phương trình (1) cho <mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math>, ta được:<mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mn>4</mn><mo>&#x2212;</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2−4−1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2=1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2−1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>�</mi><mo>+</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mn>4</mn><mo>−</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math>2x – 4 = 0.Vậy ta có thể trừ hai vế của phương trình (1) cho <mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math> để chuyển phương trình (1) về phương trình (2).b) Thay x = 2 vào phương trình (2), ta có:2 . 2 – 4 = 4 – 4 = 0.Vậy x = 2 là nghiệm của phương trình (2).c) Với x = 2 thì mẫu của phân thức <mfrac><mn>1</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math> bằng 0 nên phân thức không xác định.Vậy x = 2 không phải là nghiệm của phương trình (1).Thực hành 3 trang 8 Toán 9 Tập 1: Tìm điều kiện xác định của mỗi phương trình sau:a) <mfrac><mn>5</mn><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>14</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>5</mn></mrow></mfrac><mo>;</mo></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">5<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+7=−14<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−5;<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mrow><mi>�</mi><mo>+</mo><mn>7</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>14</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>5</mn></mrow></mfrac><mo>;</mo></math>b) <mfrac><mn>3</mn><mrow><mn>3</mn><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mi>x</mi><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mn>1.</mn></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">33<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2=<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2−1.<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><mn>3</mn><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mi>�</mi><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mn>1.</mn></math>Lời giải:a) Ta có x + 7 ≠ 0 khi x ≠ –7 và x – 5 ≠ 0 khi x ≠ 5.Vậy điều kiện xác định của phương trình là x ≠ –7 và x ≠ 5.b) Ta có 3x – 2 ≠ 0 khi <mi>x</mi><mo>&#x2260;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x≠23<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>≠</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math> và x + 2 ≠ 0 khi x ≠ –2.Vậy điều kiện xác định của phương trình là <mi>x</mi><mo>&#x2260;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x≠23<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>≠</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math> và x ≠ –2.Khám phá 3 trang 8 Toán 9 Tập 1: Cho phương trình <mfrac><mi>x</mi><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mn>1.</mn></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2=1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1+1.<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>�</mi><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mn>1.</mn></math>a) Tìm điều kiện xác định của phương trình đã cho.b) Xét các phép biến đổi như sau:<mfrac><mi>x</mi><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mn>1</mn></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2=1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1+1<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>�</mi><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mn>1</mn></math><mfrac><mi>x</mi><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2=<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>�</mi><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math><mfrac><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)=(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>x2 + x = x2 – 4x = – 4Hãy giải thích cách thực hiện mỗi phép biến đổi trên.c) x = – 4 có là nghiệm của phương trình đã cho không?Lời giải:a) Điều kiện xác định của phương trình đã cho là x – 2 ≠ 0 và x + 1 ≠ 0.Suy ra x ≠ 2 và x ≠ –1.Vậy điều kiện xác định của phương trình đã cho là x ≠ 2 và x ≠ –1.b) Cách thực hiện mỗi phép biến đổi lần lượt như sau:<mfrac><mi>x</mi><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mn>1</mn></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2=1<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1+1<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>�</mi><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mn>1</mn></math><mfrac><mi>x</mi><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2=<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>�</mi><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math> (quy đồng mẫu thức ở vế phải và rút gọn vế phải)<mfrac><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-7-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)=(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>(quy đồng mẫu thức hai phân thức)x2 + x = x2 – 4 (khử mẫu của hai phân thức ở hai vế)x = – 4 (trừ hai vế cho x2)c) Từ câu b, theo các bước biến đổi và ta thấy x = – 4 thỏa mãn điều kiện xác định của phương trình nên x = – 4 có là nghiệm của phương trình đã cho.Thực hành 4 trang 9 Toán 9 Tập 1: Giải các phương trình sau:a) <mfrac><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>=</mo><mn>2</mn><mo>;</mo></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+6<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5+32=2;<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>=</mo><mn>2</mn><mo>;</mo></math>b) <mfrac><mn>2</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mfrac><mn>3</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>x</mi><mo>&#x2212;</mo><mn>20</mn></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>.</mo></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2−3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3=3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−20(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2).<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mn>3</mn><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>�</mi><mo>−</mo><mn>20</mn></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>.</mo></math>Lời giải:a) Điều kiện xác định: x ≠ –5.Ta có: <mfrac><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>=</mo><mn>2</mn></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+6<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5+32=2<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>=</mo><mn>2</mn></math><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>&#x22C5;</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+6)2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5)+3(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5)2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5)=2⋅2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5)2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>+</mo><mn>6</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>⋅</mo><mn>2</mn><mfenced><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac></math>2(x + 6) + 3(x + 5) = 4(x + 5)2x + 12 + 3x + 15 = 4x + 205x + 27 = 4x + 20x = –7 (thỏa mãn điều kiện xác định).Vậy nghiệm của phương trình đã cho là x = –7.b) Điều kiện xác định: x ≠ 2; x ≠ 3.Ta có: <mfrac><mn>2</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mfrac><mn>3</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>x</mi><mo>&#x2212;</mo><mn>20</mn></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2−3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3=3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−20(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mn>3</mn><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>�</mi><mo>−</mo><mn>20</mn></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>&#x2212;</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>x</mi><mo>&#x2212;</mo><mn>20</mn></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)−3(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)=3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−20(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>�</mi><mo>−</mo><mn>20</mn></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>2(x – 3) – 3(x – 2) = 3x – 202x – 6 – 3x + 6 = 3x – 20–x = 3x – 20–4x = –20x = 5 (thỏa mãn điều kiện xác định).Vậy nghiệm của phương trình đã cho là x = 5.Vận dụng 2 trang 9 Toán 9 Tập 1: Hai thành phố A và B cách nhau 120 km. Một ô tô di chuyển từ A đến B, rồi quay trở về A với tổng thời gian đi và về là 4 giờ 24 phút. Tính tốc độ lúc đi của ô tô, biết tốc độ lúc về lớn hơn tốc độ lúc đi 20%.Lời giải:Gọi x (km/h) là tốc độ ô tô lúc đi (x > 0).Thời gian của ô tô lúc đi (từ A đến B) là: <mfrac><mn>120</mn><mi>x</mi></mfrac></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">120<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>120</mn><mi>�</mi></mfrac></math>(giờ).Vì tốc độ lúc về lớn hơn tốc độ lúc đi 20% nên tốc độ của ô tô lúc về là:(100% + 20%)x = 120%x = 1,2x (km/h).Thời gian của ô tô lúc về (từ B về A) là: <mfrac><mn>120</mn><mrow><mn>1,2</mn><mi>x</mi></mrow></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">1201,2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>120</mn><mrow><mn>1,2</mn><mi>�</mi></mrow></mfrac></math>(giờ).Tổng thời gian ô tô đi và về là 4 giờ 24 phút (hay <mfrac><mn>22</mn><mn>5</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">225<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>22</mn><mn>5</mn></mfrac></math>giờ) nên ta có phương trình:<mfrac><mn>120</mn><mi>x</mi></mfrac><mo>+</mo><mfrac><mn>120</mn><mrow><mn>1,2</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mn>22</mn><mn>5</mn></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">120<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1201,2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=225<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>120</mn><mi>�</mi></mfrac><mo>+</mo><mfrac><mn>120</mn><mrow><mn>1,2</mn><mi>�</mi></mrow></mfrac><mo>=</mo><mfrac><mn>22</mn><mn>5</mn></mfrac></math><mfrac><mn>120</mn><mi>x</mi></mfrac><mo>+</mo><mfrac><mn>100</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>22</mn><mn>5</mn></mfrac></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">120<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+100<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=225<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>120</mn><mi>�</mi></mfrac><mo>+</mo><mfrac><mn>100</mn><mi>�</mi></mfrac><mo>=</mo><mfrac><mn>22</mn><mn>5</mn></mfrac></math><mfrac><mn>220</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>22</mn><mn>5</mn></mfrac></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">220<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=225<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>220</mn><mi>�</mi></mfrac><mo>=</mo><mfrac><mn>22</mn><mn>5</mn></mfrac></math>x = 50 (thỏa mãn điều kiện).Vậy tốc độ lúc đi của ô tô là 50 km/h.BÀI TẬPBài 1 trang 9 Toán 9 Tập 1: Giải các phương trình:a) 5x(2x – 3) = 0;b) (2x – 5)(3x + 6) = 0;c) <mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#x2212;</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>;</mo></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">(23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−1)(12<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+3)=0;<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>�</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>;</mo></math>d) (2,5t – 7,5)(0,2t + 5) = 0.Lời giải:a) Ta có: 5x(2x – 3) = 0               5x = 0 hoặc 2x – 3 = 0               x = 0 hoặc <mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=32<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math>Vậy phương trình đã cho có hai nghiệm là x = 0 và <mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=32<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math>b) Ta có: (2x – 5)(3x + 6) = 0               2x – 5 = 0 hoặc 3x + 6 = 0               <mi>x</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math> hoặc x = –2.Vậy phương trình đã cho có hai nghiệm là <mi>x</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math> và x = –2.c) Ta có: <mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#x2212;</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">(23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−1)(12<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+3)=0<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>�</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>               <mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>&#x2212;</mo><mn>1</mn><mo>=</mo><mn>0</mn></math>" id="MathJax-Element-7-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−1=0<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>−</mo><mn>1</mn><mo>=</mo><mn>0</mn></math> hoặc <mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math>" id="MathJax-Element-8-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">12<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+3=0<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>�</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math>               <mfrac><mn>2</mn><mn>3</mn></mfrac><mi>x</mi><mo>=</mo><mn>1</mn></math>" id="MathJax-Element-9-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">23<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=1<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>�</mi><mo>=</mo><mn>1</mn></math> hoặc <mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi><mo>=</mo><mo>&#x2212;</mo><mn>3</mn></math>" id="MathJax-Element-10-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">12<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−3<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>�</mi><mo>=</mo><mo>−</mo><mn>3</mn></math>               <mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-11-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=32<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math> hoặc x = –6.Vậy phương trình đã cho có hai nghiệm là <mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-12-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=32<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math> và x = –6.d) Ta có: (2,5t – 7,5)(0,2t + 5) = 0               2,5t – 7,5 = 0 hoặc 0,2t + 5 = 0               2,5t = 7,5 hoặc 0,2t = –5               x = 5 hoặc x = –25.Vậy phương trình đã cho có hai nghiệm là x = 3 và x = –25.Bài 2 trang 9 Toán 9 Tập 1: Giải các phương trình:a) 3x(x – 4) + 7(x – 4) = 0;b) 5x(x + 6) – 2x – 12 = 0;c) x2 – x – (5x – 5) = 0;d) (3x – 2)2 – (x + 6)2 = 0.Lời giải:a) Ta có: 3x(x – 4) + 7(x – 4) = 0               (x – 4)(3x + 7) = 0               x – 4 = 0 hoặc 3x + 7 = 0               x = 4 hoặc <mi>x</mi><mo>=</mo><mo>&#x2212;</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−73<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mo>−</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></math>Vậy phương trình đã cho có hai nghiệm là x = 4 và <mi>x</mi><mo>=</mo><mo>&#x2212;</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−73<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mo>−</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></math>b) Ta có: 5x(x + 6) – 2x – 12 = 0               5x(x + 6) – 2(x + 6) = 0               (x + 6)(5x – 2) = 0               x + 6 = 0 hoặc 5x – 2 = 0               x = –6 hoặc <mi>x</mi><mo>=</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=25<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math>Vậy phương trình đã cho có hai nghiệm là x = –6 và <mi>x</mi><mo>=</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=25<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math>c) Ta có: x2 – x – (5x – 5) = 0               x(x – 1) – 5(x – 1) = 0               (x – 1)(x – 5) = 0               x – 1 = 0 hoặc x – 5 = 0               x = 1 hoặc x = 5.Vậy phương trình đã cho có hai nghiệm là x = 1 và x = 5.d) Ta có: (3x – 2)2 – (x + 6)2 = 0               (3x – 2 + x + 6)(3x – 2 – x – 6) = 0               (4x + 4)(2x – 8) = 0               8(x + 1)(x – 4) = 0               x + 1 = 0 hoặc x – 4 = 0               x = –1 hoặc x = 4.Vậy phương trình đã cho có hai nghiệm là x = –1 và x = 4.Bài 3 trang 9 Toán 9 Tập 1: Giải các phương trình:a) <mfrac><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mo>=</mo><mfrac><mn>2</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac><mo>;</mo></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3+2=2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3;<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mo>=</mo><mfrac><mn>2</mn><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac><mo>;</mo></math>b) <mfrac><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>=</mo><mn>3</mn><mo>;</mo></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=3;<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>�</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>2</mn><mi>�</mi></mfrac><mo>=</mo><mn>3</mn><mo>;</mo></math>c) <mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2+<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac></math> = 2;d) <mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mfrac><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>16</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x2212;</mo><mn>4</mn></mrow></mfrac><mo>.</mo></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2−<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2=16<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x2−4.<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>16</mn><mrow><msup><mi>�</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn></mrow></mfrac><mo>.</mo></math>Lời giải:a) Điều kiện xác định: x ≠ 3.Ta có: <mfrac><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mo>=</mo><mfrac><mn>2</mn><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3+2=2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mo>=</mo><mfrac><mn>2</mn><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac></math>            x + 5 + 2(x – 3) = 2            x + 5 + 2x – 6 = 2            3x = 3            x = 1 (thỏa mãn điều kiện xác định).Vậy nghiệm của phương trình đã cho là x = 1.b) Điều kiện xác định: x ≠ –1; x ≠ 0.Ta có: <mfrac><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>=</mo><mn>3</mn></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=3<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>�</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>2</mn><mi>�</mi></mfrac><mo>=</mo><mn>3</mn></math>            <mfrac><mrow><mi>x</mi><mfenced><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-7-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x(3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+5)<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)+2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)=3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mfenced><mrow><mn>3</mn><mi>�</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mi>�</mi><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>�</mi><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>�</mi><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>�</mi><mfenced><mrow><mi>�</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math>            x(3x + 5) + 2(x + 1) = 3x(x + 1)            3x2 + 5x + 2x + 2 = 3x2 + 3x            5x + 2x – 3x = –2            4x = –2            <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>1</mn></mrow><mn>2</mn></mfrac></math>" id="MathJax-Element-8-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−12<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></math> (thỏa mãn điều kiện xác định).Vậy nghiệm của phương trình đã cho là <mi>x</mi><mo>=</mo><mfrac><mrow><mo>&#x2212;</mo><mn>1</mn></mrow><mn>2</mn></mfrac></math>" id="MathJax-Element-9-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=−12<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></math>c) Điều kiện xác định: x ≠ 2; x ≠ 3.Ta có: <mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mn>2</mn></math>" id="MathJax-Element-10-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+3<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2+<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3=2<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mn>2</mn></math>         <mfrac><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-11-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)+(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)=2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow></mfrac></math>         <mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x2212;</mo><mn>9</mn></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x2212;</mo><mn>4</mn></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-12-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x2−9(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)+<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x2−4(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)=2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−3)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>�</mi><mn>2</mn></msup><mo>−</mo><mn>9</mn></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><msup><mi>�</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>3</mn></mrow></mfenced></mrow></mfrac></math>         x2 – 9 + x2 – 4 = 2(x – 2)(x – 3)         2x2 – 13 = 2(x2 – 5x + 6)         2x2 – 13 = 2x2 – 10x + 12         10x = 25         <mi>x</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-13-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math> (thỏa mãn điều kiện xác định).Vậy nghiệm của phương trình đã cho là <mi>x</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>" id="MathJax-Element-14-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=52<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>�</mi><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math>.d) Điều kiện xác định: x ≠ 2; x ≠ –2.Ta có: <mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac><mo>&#x2212;</mo><mfrac><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>16</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x2212;</mo><mn>4</mn></mrow></mfrac></math>" id="MathJax-Element-15-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2−<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2=16<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x2−4<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>16</mn><mrow><msup><mi>�</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn></mrow></mfrac></math>         <mfrac><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>&#x2212;</mo><mfrac><msup><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>16</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>" id="MathJax-Element-16-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2)2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)−(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)2(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)=16(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+2)(<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−2)<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mfenced><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>−</mo><mfrac><msup><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>16</mn><mrow><mfenced><mrow><mi>�</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>�</mi><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></math>         (x + 2)2 – (x – 2)2 = 16         (x + 2 + x – 2)(x + 2 – x + 2) = 16         2x . 4 = 16         8x = 16         x = 2 (không thỏa mãn điều kiện xác định).Vậy phương trình đã cho vô nghiệm.Bài 4 trang 10 Toán 9 Tập 1: Một người đi xe đạp từ A đến B cách nhau 60 km. Sau 1 giờ 40 phút, trên cùng quãng đường đó, một xe máy đi từ A đến B và đến B sớm hơn xe đạp 1 giờ. Tính vận tốc của mỗi xe, biết rằng tốc độ của xe máy gấp 3 lần tốc độ của xe đạp.Lời giải:Gọi vận tốc xe đạp là: x (km/h) (x > 0).Vận tốc xe máy là: 3x (km/h)Thời gian đi của xe đạp là: <mfrac><mn>60</mn><mi>x</mi></mfrac></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">60<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>60</mn><mi>�</mi></mfrac></math> (giờ)Thời gian đi của xe máy là: <mfrac><mn>60</mn><mrow><mn>3</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mn>20</mn><mi>x</mi></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">603<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=20<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>60</mn><mrow><mn>3</mn><mi>�</mi></mrow></mfrac><mo>=</mo><mfrac><mn>20</mn><mi>�</mi></mfrac></math> (giờ).Vì xe máy xuất phát sau xe đạp 1 giờ 40 phút (hay <mfrac><mn>5</mn><mn>3</mn></mfrac></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">53<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>3</mn></mfrac></math> giờ) và xe máy đến B sớm hơn xe đạp 1 giờ nên ta có phương trình:<mfrac><mn>60</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>+</mo><mfrac><mn>20</mn><mi>x</mi></mfrac><mo>+</mo><mn>1</mn></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">60<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=53+20<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x+1<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>60</mn><mi>�</mi></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>+</mo><mfrac><mn>20</mn><mi>�</mi></mfrac><mo>+</mo><mn>1</mn></math><mfrac><mn>60</mn><mi>x</mi></mfrac><mo>&#x2212;</mo><mfrac><mn>20</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>+</mo><mn>1</mn></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">60<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−20<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=53+1<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>60</mn><mi>�</mi></mfrac><mo>−</mo><mfrac><mn>20</mn><mi>�</mi></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>+</mo><mn>1</mn></math><mfrac><mn>40</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>8</mn><mn>3</mn></mfrac></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">40<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=83<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>40</mn><mi>�</mi></mfrac><mo>=</mo><mfrac><mn>8</mn><mn>3</mn></mfrac></math>8x = 120x = 15 (thỏa mãn điều kiện xác định)Vậy vận tốc của xe đạp là 15 km/h, vận tốc của xe máy là: 3.15 = 45 km/h.Bài 5 trang 10 Toán 9 Tập 1: Một xí nghiệp dự định chia đều 12 600 000 đồng để thưởng cho các công nhân tham gia hội thao nhân ngày thành lập xí nghiệp. Khi đến ngày hội thao chỉ có 80% số công nhân tham gia, vì thế mỗi người tham gia hội thao được nhận thêm 105 000 đồng. Tính số công nhân dự định tham gia lúc đầu.Lời giải:Gọi x là số công nhân dự định tham gia lúc đầu (x ∈ ℕ*).Theo dự định, số tiền mà mỗi công nhân được chia là: <mfrac><mrow><mn>12</mn><mtext>&#x2009;&#x2009;</mtext><mn>600</mn><mtext>&#x2009;&#x2009;</mtext><mn>000</mn></mrow><mi>x</mi></mfrac></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">12600000<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mtext>  </mtext><mn>600</mn><mtext>  </mtext><mn>000</mn></mrow><mi>�</mi></mfrac></math>(đồng).Theo thực tế, số công nhân tham gia hội thao là: 80%x = 0,8x (công nhân).Theo thực tế, số tiền mà mỗi công nhân được chia là: <mfrac><mrow><mn>12</mn><mtext>&#x2009;&#x2009;</mtext><mn>600</mn><mtext>&#x2009;&#x2009;</mtext><mn>000</mn></mrow><mrow><mn>0,8</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>15</mn><mtext>&#x2009;&#x2009;</mtext><mn>750</mn><mtext>&#x2009;&#x2009;</mtext><mn>000</mn></mrow><mi>x</mi></mfrac></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">126000000,8<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=15750000<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mtext>  </mtext><mn>600</mn><mtext>  </mtext><mn>000</mn></mrow><mrow><mn>0,8</mn><mi>�</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>15</mn><mtext>  </mtext><mn>750</mn><mtext>  </mtext><mn>000</mn></mrow><mi>�</mi></mfrac></math>(đồng).Theo đề bài ta có phương trình: <mfrac><mrow><mn>12</mn><mtext>&#x2009;&#x2009;</mtext><mn>600</mn><mtext>&#x2009;&#x2009;</mtext><mn>000</mn></mrow><mi>x</mi></mfrac><mo>=</mo><mfrac><mrow><mn>15</mn><mtext>&#x2009;&#x2009;</mtext><mn>750</mn><mtext>&#x2009;&#x2009;</mtext><mn>000</mn></mrow><mi>x</mi></mfrac><mo>&#x2212;</mo><mn>105</mn><mtext>&#x2009;&#x2009;</mtext><mn>000</mn></math>" id="MathJax-Element-3-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">12600000<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=15750000<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−105000<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mtext>  </mtext><mn>600</mn><mtext>  </mtext><mn>000</mn></mrow><mi>�</mi></mfrac><mo>=</mo><mfrac><mrow><mn>15</mn><mtext>  </mtext><mn>750</mn><mtext>  </mtext><mn>000</mn></mrow><mi>�</mi></mfrac><mo>−</mo><mn>105</mn><mtext>  </mtext><mn>000</mn></math><mfrac><mn>840</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>1050</mn><mi>x</mi></mfrac><mo>&#x2212;</mo><mn>7</mn></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">840<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=1050<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x−7<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>840</mn><mi>�</mi></mfrac><mo>=</mo><mfrac><mn>1050</mn><mi>�</mi></mfrac><mo>−</mo><mn>7</mn></math><mfrac><mn>210</mn><mi>x</mi></mfrac><mo>=</mo><mn>7</mn></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline-block; float: none; font-size: 21.78px; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; text-align: left; white-space: nowrap; word-spacing: normal;" tabindex="0">210<span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.278em; padding-top: 0.232em; white-space: pre;">x=7<span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>210</mn><mi>�</mi></mfrac><mo>=</mo><mn>7</mn></math>x = 30 (thỏa mãn điều kiện).Vậy số công nhân dự định tham gia lúc đầu là 30 người.

C1 Bài 1: Phương trình quy về phương trình bậc nhất một ẩn

Khởi động trang 6 Toán 9 Tập 1: Độ cao h (mét) của một quả bóng gôn sau khi được đánh t giây được cho bởi công thức h = t(20 – 5t). Có thể ...

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