\(\left(\dfrac{\sqrt{x}}{\sqrt{x}+2}+\dfrac{8\sqrt{x}+8}{x+2\sqrt{x}}-\dfrac{\sqrt{x}+2}{\sqrt{x}}\right):\left(\dfrac{x+\sqrt{x}+3}{x+2\sqrt{x}}+\dfrac{1}{\sqrt{x}}\right)\left(x>0;x\ne2\right)\\ =\left(\dfrac{\sqrt{x}}{\sqrt{x}+2}+\dfrac{8\sqrt{x}+8}{\sqrt{x}\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}+2}{\sqrt{x}}\right):\left(\dfrac{x+\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}+2\right)}+\dfrac{1}{\sqrt{x}}\right)\\ =\left(\dfrac{\sqrt{x}\cdot\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}+\dfrac{8\sqrt{x}+8}{\sqrt{x}\left(\sqrt{x}+2\right)}-\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}\left(\sqrt{x}+2\right)}\right):\left(\dfrac{x+\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}+2\right)}\right)\)
\(=\dfrac{x+8\sqrt{x}+8-x-\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}+2\right)}:\dfrac{x+\sqrt{x}+3+\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}+2\right)}\\ =\dfrac{7\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x+2}\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{x+2\sqrt{x}+5}\\ =\dfrac{7\sqrt{x}+4}{x+2\sqrt{x}+5}\)
