Đáp án:
$\begin{array}{l}
Dkxd:x > 0;x\# 1\\
M = \left( {\dfrac{{\sqrt x }}{{\sqrt x - 1}} - \dfrac{1}{{x - \sqrt x }}} \right):\left( {\dfrac{1}{{\sqrt x + 1}} + \dfrac{2}{{x - 1}}} \right)\\
= \dfrac{{\sqrt x .\sqrt x - 1}}{{\sqrt x \left( {\sqrt x - 1} \right)}}:\dfrac{{\sqrt x - 1 + 2}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x \left( {\sqrt x - 1} \right)}}.\dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}{{\sqrt x + 1}}\\
= \dfrac{{x - 1}}{{\sqrt x }}\\
M > 0\\
\Leftrightarrow M > 0\\
\Leftrightarrow \dfrac{{x - 1}}{{\sqrt x }} > 0\\
\Leftrightarrow x - 1 > 0\\
\Leftrightarrow x > 1\\
Vay\,x > 1
\end{array}$
