$\begin{array}{l}\dfrac{2x - \sqrt x + 2}{x - 4} + \dfrac{1}{\sqrt x + 2} - \dfrac{\sqrt x}{\sqrt x -2}\qquad (x \geq 0;\, x \ne 2)\\ = \dfrac{2x - \sqrt x + 2}{(\sqrt x - 2)(\sqrt x + 2)} + \dfrac{\sqrt x - 2}{(\sqrt x - 2)(\sqrt x + 2)} - \dfrac{\sqrt x(\sqrt x + 2)}{(\sqrt x - 2)(\sqrt x + 2)}\\ = \dfrac{2x - \sqrt x + 2 + \sqrt x - 2 - x - 2\sqrt x}{(\sqrt x - 2)(\sqrt x + 2)}\\ = \dfrac{x - 2\sqrt x}{(\sqrt x - 2)(\sqrt x + 2)}\\ = \dfrac{\sqrt x(\sqrt x - 2)}{(\sqrt x - 2)(\sqrt x + 2)}\\ = \dfrac{\sqrt x}{\sqrt x + 2}\end{array}$
