Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
P = \frac{{\sqrt x + 1}}{{\sqrt x - 2}} + \frac{{2\sqrt x }}{{\sqrt x + 2}} + \frac{{2 + 5\sqrt x }}{{4 - x}}\\
= \frac{{\sqrt x + 1}}{{\sqrt x - 2}} + \frac{{2\sqrt x }}{{\sqrt x + 2}} - \frac{{5\sqrt x + 2}}{{x - 4}}\\
= \frac{{\sqrt x + 1}}{{\sqrt x - 2}} + \frac{{2\sqrt x }}{{\sqrt x + 2}} - \frac{{5\sqrt x + 2}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x + 2} \right) + 2\sqrt x \left( {\sqrt x - 2} \right) - \left( {5\sqrt x + 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{x + 3\sqrt x + 2 + 2x - 4\sqrt x - 5\sqrt x - 2}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{3x - 6\sqrt x }}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{3\sqrt x \left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{3\sqrt x }}{{\sqrt x + 2}}\\
b,\\
P = 2 \Leftrightarrow \frac{{3\sqrt x }}{{\sqrt x + 2}} = 2\\
\Leftrightarrow 3\sqrt x = 2\sqrt x + 4\\
\Leftrightarrow \sqrt x = 4\\
\Leftrightarrow x = 16\,\,\,\,\,\,\left( {t/m} \right)
\end{array}\)
