Question

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

Answer 1

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

\(=\dfrac{-4\left(x-2\sqrt{x}-2\right)}{4-x}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{3-\sqrt{x}}\)

\(=\dfrac{4\left(x-2\sqrt{x}-2\right)}{\sqrt{x}+2}\cdot\dfrac{\sqrt{x}}{3-\sqrt{x}}=\dfrac{4\sqrt{x}\left(x-2\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(3-\sqrt{x}\right)}\)