\(C=\left(\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}-\dfrac{x}{4-x}\right):\dfrac{1}{\sqrt{x-2}}\left(x\ge2;x\ne4\right)\\ =\left[\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right]:\dfrac{1}{\sqrt{x-2}}\\ =\dfrac{\sqrt{x}+2+\sqrt{x}-2+x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\dfrac{1}{\sqrt{x-2}}\\ =\dfrac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\dfrac{1}{\sqrt{x-2}}\\ =\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\sqrt{x-2}\\ =\dfrac{\sqrt{x}}{\sqrt{x}-2}\cdot\sqrt{x-2}\\ =\dfrac{\sqrt{x^2-2x}}{\sqrt{x}-2}\)
