1) \(A=\dfrac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}+\dfrac{2\sqrt{2}}{\sqrt{10}-\sqrt{2}}\)
\(=\dfrac{\sqrt{2}\left(\sqrt{3}-\sqrt{5}\right)}{-2}+\dfrac{2\sqrt{2}\left(\sqrt{10}+\sqrt{2}\right)}{8}\)
\(=\dfrac{\sqrt{6}-\sqrt{10}}{-2}+\dfrac{\sqrt{2}\left(\sqrt{10}+\sqrt{2}\right)}{4}\)
\(=-\dfrac{\sqrt{6}-\sqrt{10}}{2}+\dfrac{\sqrt{20}+2}{4}\)
\(=-\dfrac{\sqrt{6}-\sqrt{10}}{2}+\dfrac{2\sqrt{5}+2}{4}\)
\(=-\dfrac{\sqrt{6}-\sqrt{10}}{2}+\dfrac{2\left(\sqrt{5}+1\right)}{4}\)
\(=-\dfrac{\sqrt{6}-\sqrt{10}}{2}+\dfrac{\sqrt{5}+1}{2}\)
\(=\dfrac{-\left(\sqrt{6}-\sqrt{10}\right)+\sqrt{5}+1}{2}\)
\(=\dfrac{-\sqrt{6}+\sqrt{10}+\sqrt{5}+1}{2}\)
2) \(\left(\dfrac{\sqrt{a}}{1-\sqrt{a}}+\dfrac{\sqrt{a}}{a-1}\right):\dfrac{\sqrt{a}}{a-1}\)
\(=\left(\dfrac{\sqrt{a}}{-\left(\sqrt{a}-1\right)}+\dfrac{\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right):\dfrac{\sqrt{a}}{a-1}\)
\(=\left(-\dfrac{\sqrt{a}}{\sqrt{a}-1}+\dfrac{\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right):\dfrac{\sqrt{a}}{a-1}\)
\(=\dfrac{-\sqrt{a}\left(\sqrt{a}+1\right)+\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}:\dfrac{\sqrt{a}}{a-1}\)
\(=\dfrac{-a-\sqrt{a}+\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}:\dfrac{\sqrt{a}}{a-1}\)
\(=\dfrac{-a}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}:\dfrac{\sqrt{a}}{a-1}\)
\(=\dfrac{-a}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\cdot\dfrac{a-1}{\sqrt{a}}\)
\(=-\dfrac{a}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}}\)
\(=-a\cdot\dfrac{1}{\sqrt{a}}\)
\(=-\dfrac{a}{\sqrt{a}}\)
\(=-\dfrac{a\sqrt{a}}{a}\)
\(=-\sqrt{a}\)
