Đáp án:
$\begin{array}{l}
P = \dfrac{{x\sqrt x - \sqrt x }}{{x\sqrt x - 1}}\\
= \dfrac{{\sqrt x \left( {x - 1} \right)}}{{\left( {\sqrt x - 1} \right)\left( {x + \sqrt x + 1} \right)}}\\
= \dfrac{{\sqrt x \left( {\sqrt x + 1} \right)}}{{x + \sqrt x + 1}}\\
= \dfrac{{x + \sqrt x }}{{x + \sqrt x + 1}}\\
= \dfrac{{x + \sqrt x + 1 - 1}}{{x + \sqrt x + 1}}\\
= 1 - \dfrac{1}{{x + \sqrt x + 1}}\\
Do:\sqrt x \ge 0\\
\Rightarrow x + \sqrt x + 1 \ge 1\\
\Rightarrow \dfrac{1}{{x + \sqrt x + 1}} \le 1\\
\Rightarrow - \dfrac{1}{{x + \sqrt x + 1}} \ge - 1\\
\Rightarrow 1 - \dfrac{1}{{x + \sqrt x + 1}} \ge 1 - 1 = 0\\
\Rightarrow P \ge 0\\
\Rightarrow GTNN:P = 0\,khi:x = 0
\end{array}$
