Question

Answer 1

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

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

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

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