Question

(X/X-4 -√x/√x-2) / √x/√x-2

Answer 1

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

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

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

\(=\dfrac{-2\sqrt{x}}{x-4}:\dfrac{\sqrt{x}}{\sqrt{x}-2}\)

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

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

Answer 2

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

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