Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
DKXD:\,\,\,\left\{ \begin{array}{l}
x \ge 0\\
\sqrt x - 2 \ne 0\\
\sqrt x \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x > 0\\
x \ne 4
\end{array} \right.\\
b,\\
M = \dfrac{{\sqrt x }}{{\sqrt x - 2}} - \dfrac{{4\sqrt x - 4}}{{\sqrt x .\left( {\sqrt x - 2} \right)}}\\
= \dfrac{{{{\sqrt x }^2} - \left( {4\sqrt x - 4} \right)}}{{\sqrt x .\left( {\sqrt x - 2} \right)}}\\
= \dfrac{{x - 4\sqrt x + 4}}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{{{\left( {\sqrt x - 2} \right)}^2}}}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{\sqrt x - 2}}{{\sqrt x }}\\
c,\\
M > 0 \Leftrightarrow \dfrac{{\sqrt x - 2}}{{\sqrt x }} > 0\\
\sqrt x > 0 \Rightarrow \sqrt x - 2 > 0\\
\Leftrightarrow \sqrt x > 2\\
\Leftrightarrow x > 4
\end{array}\)
