\(P=\dfrac{\sqrt{x}-2+\sqrt{x}+2}{x-4}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}}\)
\(=\dfrac{2\sqrt{x}}{\sqrt{x}}\cdot\dfrac{1}{\sqrt{x}+2}=\dfrac{2}{\sqrt{x}+2}\)
\(P=\left(\dfrac{1}{\sqrt{x}+2}+\dfrac{1}{\sqrt{x}-2}\right)\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}}\)
\(P=\left[\dfrac{\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\dfrac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right]\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}}\)
\(P=\dfrac{\sqrt{x}-2+\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}}\)
\(P=\dfrac{2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}}\)
\(P=\dfrac{2\sqrt{x}\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(P=\dfrac{2}{\sqrt{x}+2}\)
