1) \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}=\dfrac{\left(\sqrt{5}-\sqrt{3}\right)\sqrt{2}}{2}=\dfrac{\sqrt{10}-\sqrt{6}}{2}\)
2) \(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{2+5\sqrt{x}}{4-x}\)
\(=-\dfrac{\sqrt{x}+1}{2-\sqrt{x}}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{2+5\sqrt{x}}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\)
\(=\dfrac{-\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)+2\sqrt{x}\left(2-\sqrt{x}\right)+2+5\sqrt{x}}{\left(2-\sqrt{x}\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-\left(x+\sqrt{x}+2\sqrt{x}+2\right)+4\sqrt{x}-2x+2+5\sqrt{x}}{-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-\left(x+3\sqrt{x}+2\right)+4\sqrt{x}-2x+2+5\sqrt{x}}{-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-x-3\sqrt{x}-2+4\sqrt{x}-2x+2+5\sqrt{x}}{-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-3x+6\sqrt{x}}{-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-3\sqrt{x}\left(\sqrt{x}-2\right)}{-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-3\sqrt{x}\cdot\left(-1\right)}{\sqrt{x}+2}\)
\(=\dfrac{3\sqrt{x}}{\sqrt{x}+2}\)
