Đáp án:
\(P = \dfrac{{x - 1}}{{\sqrt x }}\)
Giải thích các bước giải:
\(\begin{array}{l}
P = \left[ {\dfrac{{\sqrt x }}{{\sqrt x - 1}} - \dfrac{1}{{\sqrt x \left( {\sqrt x - 1} \right)}}} \right]:\left[ {\dfrac{1}{{\sqrt x + 1}} + \dfrac{2}{{x - 1}}} \right]\\
= \left[ {\dfrac{{x - 1}}{{\sqrt x \left( {\sqrt x - 1} \right)}}} \right]:\dfrac{{\sqrt x - 1 + 2}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{x - 1}}{{\sqrt x \left( {\sqrt x - 1} \right)}}.\dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}{{\sqrt x + 1}}\\
= \dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}{{\sqrt x \left( {\sqrt x - 1} \right)}}.\dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}{{\sqrt x + 1}}\\
= \dfrac{{\sqrt x + 1}}{{\sqrt x }}.\left( {\sqrt x - 1} \right)\\
= \dfrac{{x - 1}}{{\sqrt x }}
\end{array}\)
