Question

Answer 1

a) Ta có: \(V=\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{x}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)

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

\(=\dfrac{x-\sqrt{x}+1}{x\left(\sqrt{x}-1\right)}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}{3}\)

\(=\dfrac{\left(x-\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{3x}\)