Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
A = \left( {\dfrac{1}{{\sqrt x - 1}} - \dfrac{{\sqrt x }}{{x - 1}}} \right):\dfrac{1}{{\sqrt x + 1}}\,\,\,\,\,\,\,\,\,\,\,\,\,\left( \begin{array}{l}
x \ge 0\\
x \ne 1
\end{array} \right)\\
= \left( {\dfrac{1}{{\sqrt x - 1}} - \dfrac{{\sqrt x }}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}} \right):\dfrac{1}{{\sqrt x + 1}}\\
= \dfrac{{\left( {\sqrt x + 1} \right) - \sqrt x }}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}:\dfrac{1}{{\sqrt x + 1}}\\
= \dfrac{1}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}.\left( {\sqrt x + 1} \right)\\
= \dfrac{1}{{\sqrt x - 1}}\\
b,\\
A < 0 \Leftrightarrow \dfrac{1}{{\sqrt x - 1}} < 0 \Leftrightarrow \sqrt x - 1 < 0\\
\Leftrightarrow \sqrt x < 1 \Leftrightarrow 0 \le x < 1
\end{array}\)
