Hướng dẫn Giải Bài 32 (Trang 50, SGK Toán 8, Tập 1)

Đố. Đố em tính nhanh được tổng <math xmlns="http://www.w3.org/1998/Math/MathML"><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><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced></mrow></mfrac></math>. Giải <math xmlns="http://www.w3.org/1998/Math/MathML"><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><mn>1</mn><mi>x</mi></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</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>1</mn><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfrac></math> ........................................................... <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math> Do đó: <math xmlns="http://www.w3.org/1998/Math/MathML"><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><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>6</mn><mo>-</mo><mi>x</mi></mrow><mrow><mi>x</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mn>6</mn><mrow><mi>x</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>)</mo></mrow></mfrac></math>