Question

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

rút gọn C

Answer 1

Điều kiện: \(\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\)

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

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

\(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{2\sqrt{x}}.\left[-\dfrac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}\right]\)

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

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