Hướng dẫn giải Bài 10 (Trang 40 SGK Toán Đại số 8, Tập 1)

Đố. Đố em rút gọn được phân thức. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>7</mn></msup><mo>+</mo><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><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>; Giải  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>7</mn></msup><mo>+</mo><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><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><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mn>6</mn></msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><msup><mi>x</mi><mn>4</mn></msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><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></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mfenced><mrow><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><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></mfrac><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mn>4</mn></msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></math>