Đáp án: $P = \dfrac{{\sqrt x }}{{1 - \sqrt x }}$
Giải thích các bước giải:
$\begin{array}{l}
P = \left( {\dfrac{{x\sqrt x }}{{x\sqrt x - 1}} + \dfrac{{\sqrt x }}{{1 - \sqrt x }}} \right):\dfrac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\\
= \dfrac{{x\sqrt x - \sqrt x \left( {x + \sqrt x + 1} \right)}}{{\left( {\sqrt x - 1} \right)\left( {x + \sqrt x + 1} \right)}}.\dfrac{{x + \sqrt x + 1}}{{\sqrt x + 1}}\\
= \dfrac{{x\sqrt x - x\sqrt x - x - \sqrt x }}{{\sqrt x - 1}}.\dfrac{1}{{\sqrt x + 1}}\\
= \dfrac{{ - \sqrt x \left( {\sqrt x + 1} \right)}}{{\sqrt x - 1}}.\dfrac{1}{{\sqrt x + 1}}\\
= \dfrac{{ - \sqrt x }}{{\sqrt x - 1}}\\
= \dfrac{{\sqrt x }}{{1 - \sqrt x }}
\end{array}$
