ĐK: \(x\ge0,x\ne4\)
\(\dfrac{1}{\sqrt{x}-2}+\dfrac{5\sqrt{x}-4}{2\sqrt{x}-x}=\dfrac{-1}{2-\sqrt{x}}+\dfrac{5\sqrt{x}-4}{\sqrt{x}\left(2-\sqrt{x}\right)}=\dfrac{-\sqrt{x}+5\sqrt{x}-4}{\sqrt{x}\left(2-\sqrt{x}\right)}=\dfrac{4\sqrt{x}-4}{\sqrt{x}\left(2-\sqrt{x}\right)}=\dfrac{4\left(\sqrt{x}-1\right)}{\sqrt{x}\left(2-\sqrt{x}\right)}\)
\(\dfrac{2+\sqrt{x}}{\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}-2}=\dfrac{2+\sqrt{x}}{\sqrt{x}}+\dfrac{\sqrt{x}}{2-\sqrt{x}}=\dfrac{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)+\sqrt{x}.\sqrt{x}}{\sqrt{x}\left(2-\sqrt{x}\right)}=\dfrac{4-x+x}{\sqrt{x}\left(2-\sqrt{x}\right)}=\dfrac{4}{\sqrt{x}\left(2-\sqrt{x}\right)}\)
\(\left(\dfrac{2}{\sqrt{x}-2}+\dfrac{5\sqrt{x}-4}{2\sqrt{x}-x}\right):\left(\dfrac{2+\sqrt{x}}{\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)=\dfrac{4\left(\sqrt{x}-1\right)}{\sqrt{x}\left(2-\sqrt{x}\right)}:\dfrac{4}{\sqrt{x}\left(2-\sqrt{x}\right)}=\dfrac{4\left(\sqrt{x}-1\right)}{\sqrt{x}\left(2-\sqrt{x}\right)}.\dfrac{\sqrt{x}\left(2-\sqrt[]{x}\right)}{4}=\sqrt{x}-1\)
