Giải thích các bước giải:
a,
ĐKXĐ: \(\left\{ \begin{array}{l}
x \ge 0\\
x \ne 4
\end{array} \right.\)
Ta có:
\(\begin{array}{l}
P = \frac{x}{{x - 4}} - \frac{1}{{2 - \sqrt x }} + \frac{1}{{\sqrt x + 2}}\\
= \frac{x}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}} + \frac{1}{{\sqrt x - 2}} + \frac{1}{{\sqrt x + 2}}\\
= \frac{{x + \left( {\sqrt x + 2} \right) + \left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{x + 2\sqrt x }}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{\sqrt x \left( {\sqrt x + 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{\sqrt x }}{{\sqrt x - 2}}\\
b,\\
P < \frac{2}{5} \Leftrightarrow \frac{{\sqrt x }}{{\sqrt x - 2}} < \frac{2}{5}\\
\Leftrightarrow \frac{{\sqrt x }}{{\sqrt x - 2}} - \frac{2}{5} < 0\\
\Leftrightarrow \frac{{5\sqrt x - 2\left( {\sqrt x - 2} \right)}}{{5\left( {\sqrt x - 2} \right)}} < 0\\
\Leftrightarrow \frac{{3\sqrt x + 4}}{{5\left( {\sqrt x - 2} \right)}} < 0\\
3\sqrt x + 4 > 0,\,\,\,\forall x \ge 0,\,x \ne 4\\
\Rightarrow \sqrt x - 2 < 0 \Leftrightarrow \sqrt x < 2 \Leftrightarrow x < 4
\end{array}\)
