Đáp án: $\left| P \right| = P$
Giải thích các bước giải:
$\begin{array}{l}
B3)\\
Dkxd:x \ge 0;x \ne 25\\
P = A - B\\
= \left( {\dfrac{{15 - \sqrt x }}{{x - 25}} + \dfrac{2}{{\sqrt x + 5}}} \right):\dfrac{{\sqrt x + 1}}{{\sqrt x - 5}} - \dfrac{{1 - \sqrt x }}{{1 + \sqrt x }}\\
= \dfrac{{15 - \sqrt x + 2\left( {\sqrt x - 5} \right)}}{{\left( {\sqrt x - 5} \right)\left( {\sqrt x + 5} \right)}}.\dfrac{{\sqrt x - 5}}{{\sqrt x + 1}} + \dfrac{{\sqrt x - 1}}{{\sqrt x + 1}}\\
= \dfrac{{\sqrt x + 5}}{{\sqrt x + 5}}.\dfrac{1}{{\sqrt x + 1}} + \dfrac{{\sqrt x - 1}}{{\sqrt x + 1}}\\
= \dfrac{1}{{\sqrt x + 1}} + \dfrac{{\sqrt x - 1}}{{\sqrt x + 1}}\\
= \dfrac{{\sqrt x }}{{\sqrt x + 1}}\\
Do:x \ge 0\\
\Leftrightarrow \left\{ \begin{array}{l}
\sqrt x \ge 0\\
\sqrt x + 1 > 0
\end{array} \right.\\
\Leftrightarrow \dfrac{{\sqrt x }}{{\sqrt x + 1}} \ge 0\\
\Leftrightarrow P \ge 0\\
\Leftrightarrow \left| P \right| = P
\end{array}$
