Đáp án:
$P =\dfrac{\sqrt x-2}{3\sqrt x}$
Giải thích các bước giải:
$\begin{array}{l}P = \left(\dfrac{1}{\sqrt x - 1} - \dfrac{1}{\sqrt x}\right):\left(\dfrac{\sqrt x + 1}{\sqrt x -2} - \dfrac{\sqrt x+2}{\sqrt x-1}\right)\qquad (x >0; x \ne 1;\, x \ne 4)\\ \to P = \left[\dfrac{\sqrt x}{\sqrt x(\sqrt x - 1)} - \dfrac{\sqrt x - 1}{\sqrt x(\sqrt x-1)}\right]:\left[\dfrac{(\sqrt x + 1)(\sqrt x-1)}{(\sqrt x -2)(\sqrt x-1)} - \dfrac{(\sqrt x+2)(\sqrt x - 2)}{(\sqrt x-1)(\sqrt x-1)}\right]\\ \to P= \left[\dfrac{\sqrt x- (\sqrt x-1)}{\sqrt x(\sqrt x - 1)} \right]:\left[\dfrac{x - 1 - (x - 4)}{(\sqrt x -2)(\sqrt x-1)} \right]\\ \to P = \dfrac{1}{\sqrt x(\sqrt x-1)}:\dfrac{3}{(\sqrt x-2)(\sqrt x-1)}\\ \to P = \dfrac{1}{\sqrt x(\sqrt x-1)}\cdot \dfrac{(\sqrt x-2)(\sqrt x-1)}{3}\\ \to P =\dfrac{\sqrt x-2}{3\sqrt x}\end{array}$
