\(B=\left(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{x}+2}\right):\dfrac{2\sqrt{x}}{x+2\sqrt{x}}\) (\(x>0\))
\(B=\left[\dfrac{\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\right]\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{2\sqrt{x}}\)
\(B=\dfrac{\sqrt{x}+2+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}+2}{2}\)
\(B=\dfrac{2\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}+2}{2}\)
\(B=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
\(B=\dfrac{\sqrt{x}+2+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\dfrac{x+2\sqrt{x}}{2\sqrt{x}}\)
\(=\dfrac{2\sqrt{x}+2}{2\sqrt{x}}=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
