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