$\quad P = \left(\dfrac{4\sqrt x}{\sqrt x +2}-\dfrac{8x}{x-4}\right)\ :\ \left(\dfrac{\sqrt x +2}{\sqrt x-2} + 3\right)\quad (x\geqslant 0;\ x\ne 1;x \ne 4)$
$\to P = \dfrac{4\sqrt x\left(\sqrt x -2\right)- 8x}{\left(\sqrt x -2\right)\left(\sqrt x +2\right)}\ :\ \dfrac{\sqrt x +2 + 3\left(\sqrt x -2\right)}{\sqrt x+2}$
$\to P = \dfrac{-4x - 8\sqrt x}{\left(\sqrt x -2\right)\left(\sqrt x +2\right)}\cdot \dfrac{\sqrt x +2}{4\sqrt x - 4}$
$\to P = \dfrac{-4\sqrt x \left(\sqrt x -2\right)}{\left(\sqrt x -2\right)\left(\sqrt x +2\right)}\cdot \dfrac{\sqrt x +2}{4\left(\sqrt x -1\right)}$
$\to P = \dfrac{- \sqrt x}{\sqrt x -1}$
$b)$
$\quad P = -4$
$\to -\dfrac{\sqrt x}{\sqrt x -1}= -4$
$\to \sqrt x -1 =\dfrac14\sqrt x$
$\to \dfrac34\sqrt x = 1$
$\Leftrightarrow \sqrt x =\dfrac43$
$\to x =\dfrac{16}{9}$ (nhận)
Vậy $x=\dfrac{16}{9}$ khi $P = -4$
