F = \(\left(\frac{\sqrt{x}}{\sqrt{x}+2}-\frac{x+2}{x-4}\right):\left(\frac{2\sqrt{x}-1}{x-2\sqrt{x}}-\frac{1}{\sqrt{x}}\right)\)
= \(\frac{\sqrt{x}\left(\sqrt{x}-2\right)-x-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}:\frac{2\sqrt{x}-1-\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
= \(\frac{-2\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}.\frac{\left(\sqrt{x}-2\right)\sqrt{x}}{\sqrt{x}+1}\)
= \(\frac{-2\sqrt{x}}{\sqrt{x}+2}\)