Hướng dẫn Giải Bài 18 (Trang 43, SGK Toán 8, Tập 1)

Quy đồng mẫu thức hai phân thức: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>x</mi></mrow><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow></mfrac></math>;                                   b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math>. Giải a) Ta có <ul> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn><mo>=</mo><mn>2</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>=</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></li> <li>MTC=<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>2</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow></mfenced></math></li> <li>Quy đồng <ul> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>x</mi></mrow><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>x</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>x</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow></mfenced></mrow></mfrac></math></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow></mfenced></mrow></mfrac></math></li> </ul> </li> </ul> b) Ta có <ul> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>4</mn><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></math></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>3</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></li> <li>MTC=<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></msup></math></li> <li>Quy đồng <ul> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>.</mo><mn>3</mn></mrow><mrow><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>.</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mn>3</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac></math></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mn>3</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>)</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mn>3</mn><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac></math></li> </ul> </li> </ul>