Hướng dẫn Giải Bài 51 (trang 30, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 51 (Trang 30 SGK Toán 9, Tập 1)

Bài 51 (Trang 30 SGK Toán 9, Tập 1): Trục căn thức ở mẫu với giả thiết các biểu thức chữ đều có nghĩa: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>1</mn></mrow></mfrac><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfrac><mi mathvariant="normal">b</mi><mrow><mn>3</mn><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfrac><mi mathvariant="normal">p</mi><mrow><mn>2</mn><msqrt><mi mathvariant="normal">p</mi></msqrt><mo>-</mo><mn>1</mn></mrow></mfrac><mo>;</mo></math>   Hướng dẫn giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>3</mn><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>3</mn><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>3</mn><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>3</mn><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>3</mn><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>(</mo><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo><mo>(</mo><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mo>-</mo><msqrt><mn>3</mn></msqrt><mo>)</mo><mo>(</mo><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>4</mn><mo>+</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>3</mn></mrow><mrow><msup><mn>2</mn><mn>2</mn></msup><mo>-</mo><msup><mrow><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mn>7</mn><mo> </mo><mo>+</mo><mo> </mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">b</mi><mrow><mn>3</mn><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi mathvariant="normal">b</mi><mo>(</mo><mn>3</mn><mo>-</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><mn>3</mn><mo>+</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo><mo>(</mo><mn>3</mn><mo>-</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi mathvariant="normal">b</mi><mo>(</mo><mn>3</mn><mo>-</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow><mrow><msup><mn>3</mn><mn>2</mn></msup><mo>-</mo><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi mathvariant="normal">b</mi><mo>(</mo><mn>3</mn><mo>-</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>)</mo></mrow><mrow><mn>9</mn><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac><mo>.</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">p</mi><mrow><mn>2</mn><msqrt><mi mathvariant="normal">p</mi></msqrt><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi mathvariant="normal">p</mi><mo>(</mo><mn>2</mn><msqrt><mi mathvariant="normal">p</mi></msqrt><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><msqrt><mi mathvariant="normal">p</mi></msqrt><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><msqrt><mi mathvariant="normal">p</mi></msqrt><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi mathvariant="normal">p</mi><mo>(</mo><mn>2</mn><msqrt><mi mathvariant="normal">p</mi></msqrt><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><msup><mrow><mo>(</mo><mn>2</mn><msqrt><mi mathvariant="normal">p</mi></msqrt><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">p</mi><msqrt><mi mathvariant="normal">p</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">p</mi></mrow><mrow><mn>4</mn><mi mathvariant="normal">p</mi><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn></mrow></mfrac><mo>.</mo></math>