Question

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

B = \(\dfrac{y-5\sqrt{x}}{x-16}\) - \(\dfrac{2}{4-\sqrt{x}}\) + \(\dfrac{3}{\sqrt{x}+4}\)

Answer 1

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

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

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

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