\(=\dfrac{\sqrt{x}+2-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\sqrt{x}+2}{2}=\dfrac{4}{\sqrt{x}-2}.\dfrac{1}{2}=\dfrac{2}{\sqrt{x}-2}\)
\(\left(\dfrac{1}{\sqrt{x}-2}-\dfrac{1}{\sqrt{x}+2}\right).\left(\dfrac{\sqrt{x}+2}{2}\right)^2\\ =\left(\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}+2\right)}\right).\dfrac{\left(\sqrt{x}+2\right)^2}{4}\)
\(=\dfrac{\sqrt{x}+2-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\left(\sqrt{x}+2\right)^2}{4}\)
\(=\dfrac{4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\left(\sqrt{x}+2\right)^2}{4}\)
\(=\dfrac{4\left(\sqrt{x}+2\right)^2}{4\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}+2}{\sqrt{x}-2}\)
