Giải thích các bước giải:
$\begin{array}{l}
A = \frac{x}{{\sqrt x - 1}} - \frac{{2x - \sqrt x }}{{x - \sqrt x }}\left( {x > 0;x \ne 1} \right)\\
a)A = \frac{x}{{\sqrt x - 1}} - \frac{{\sqrt x \left( {2\sqrt x - 1} \right)}}{{\sqrt x \left( {\sqrt x - 1} \right)}}\\
= \frac{x}{{\sqrt x - 1}} - \frac{{2\sqrt x - 1}}{{\sqrt x - 1}}\\
= \frac{{x - 2\sqrt x + 1}}{{\sqrt x - 1}}\\
= \frac{{{{\left( {\sqrt x - 1} \right)}^2}}}{{\sqrt x - 1}}\\
= \sqrt x - 1\\
b)x > 0;x \ne 1\\
x = 3 + 2\sqrt 2 \left( {tmdk} \right)\\
\Rightarrow x = 2 + 2\sqrt 2 + 1 = {\left( {\sqrt 2 + 1} \right)^2}\\
\Rightarrow \sqrt x = \sqrt 2 + 1\\
\Rightarrow A = \sqrt 2 + 1 - 1\\
\Rightarrow A = \sqrt 2
\end{array}$
