Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l}
x > 0\\
x \ne 1
\end{array} \right.\)
Ta có:
\[\begin{array}{l}
A = \frac{x}{{\sqrt x + 1}} - \frac{{2x - \sqrt x }}{{x - \sqrt x }}\\
= \frac{x}{{\sqrt x + 1}} - \frac{{\sqrt x \left( {2\sqrt x - 1} \right)}}{{\sqrt x \left( {\sqrt x - 1} \right)}}\\
= \frac{x}{{\sqrt x + 1}} - \frac{{2\sqrt x - 1}}{{\sqrt x - 1}}\\
= \frac{{x\left( {\sqrt x - 1} \right) - \left( {2\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \frac{{x\sqrt x - x - \left( {2x + \sqrt x - 1} \right)}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \frac{{x\sqrt x - 3x - \sqrt x + 1}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}
\end{array}\]
