Hướng dẫn Giải Bài 58 (Trang 62, SGK Toán 8, Tập 1)

Thực hiện các phép tính sau: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfrac><mrow><mn>4</mn><mi>x</mi></mrow><mrow><mn>10</mn><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfrac><mo>;</mo></math>                                     b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mo>-</mo><mi>x</mi></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfenced><mrow><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>.</mo><mfenced><mrow><mfrac><mn>1</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></mrow></mfenced></math>. Giải a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfrac><mrow><mn>4</mn><mi>x</mi></mrow><mrow><mn>10</mn><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>.</mo><mfrac><mrow><mn>10</mn><mi>x</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>4</mn><mi>x</mi></mrow></mfrac></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>-</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>.</mo><mfrac><mrow><mn>5</mn><mo>(</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>4</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>8</mn><mi>x</mi><mo>.</mo><mn>5</mn><mo>(</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>.</mo><mn>4</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mn>10</mn><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mo>-</mo><mi>x</mi></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfenced><mrow><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mfenced open="[" close="]"><mrow><mfrac><mn>1</mn><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></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></mrow></mfenced><mo>:</mo><mfrac><mrow><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi></mrow><mi>x</mi></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mi>x</mi><mo>(</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>x</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>.</mo><mfrac><mi>x</mi><mrow><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>x</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mfenced><mrow><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>.</mo><mfenced><mrow><mfrac><mn>1</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></mrow></mfenced><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>.</mo><mfenced open="[" close="]"><mrow><mfrac><mn>1</mn><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac></mrow></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>x</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>.</mo><mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>.</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>x</mi><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>.</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>.</mo><mn>2</mn></mrow><mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mn>2</mn><mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>-</mo><mn>2</mn><mi>x</mi></mrow><mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac></math>