Giải thích các bước giải:
a) $P\left ( x \right ) = \dfrac{2\sqrt{x}}{x + 2\sqrt{x}} + \dfrac{x - 1}{x + 3\sqrt{x} + 2}$ $(x > 0)$
$= \dfrac{2\sqrt{x}}{\sqrt{x}\left ( \sqrt{x} + 2 \right )} + \dfrac{\left ( \sqrt{x} - 1 \right )\left ( \sqrt{x} + 1 \right )}{\left ( \sqrt{x} + 2 \right )\left ( \sqrt{x} + 1 \right )}$
$= \dfrac{2}{\sqrt{x} + 2} + \dfrac{\sqrt{x} - 1}{\sqrt{x} + 2}$
$= \dfrac{2 + \sqrt{x} - 1}{\sqrt{x} + 2}$
$= \dfrac{\sqrt{x} + 1}{\sqrt{x} + 2}$
b) $P\left ( x \right ) = \dfrac{4}{5}$ khi và chỉ khi:
$\dfrac{\sqrt{x} + 1}{\sqrt{x} + 2} = \dfrac{4}{5}$
$\Leftrightarrow 4\left ( \sqrt{x} + 2 \right ) = 5\left ( \sqrt{x} + 1 \right ) $
$\Leftrightarrow 4\sqrt{x} + 8 = 5\sqrt{x} + 5$
$\Leftrightarrow \sqrt{x} = 3$
$\Leftrightarrow x = 9 (tm)$
