Question

                            rút gọn P 

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >4\end{matrix}\right.\)

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

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

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