Question

rút gọn biểu thức

A=\(\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{8\sqrt{x}}{x-1}\right):\dfrac{4\sqrt{x}-8}{1-x}\)

Answer 1

A=(\(\dfrac{\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)-\(\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)-\(\dfrac{8\sqrt{x}}{x-1}\)):\(\dfrac{4\sqrt{x}-8}{1-x}\)

A=\(\dfrac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}+1\right)^2-8\sqrt{x}}{x-1}\cdot\dfrac{x-1}{8-4\sqrt{x}}\)

A=\(\dfrac{\left(\sqrt{x}-1+\sqrt{x}+1\right)\left(\sqrt{x}-1-\sqrt{x}-1\right)}{4\left(2-\sqrt{x}\right)}\)

A=\(\dfrac{2\sqrt{x}\left(-2\right)}{4\left(2-\sqrt{x}\right)}\)

A=\(\dfrac{-\sqrt{x}}{2-\sqrt{x}}=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)