\(\left(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{\sqrt{30}-\sqrt{6}}{\sqrt{5}-1}\right):\dfrac{1}{2\sqrt{5}-\sqrt{6}}\)
\(=\left(\dfrac{2\sqrt{5}\cdot\sqrt{5}+\sqrt{2}\cdot2\sqrt{5}}{\sqrt{5}+\sqrt{2}}+\dfrac{\sqrt{5}\cdot\sqrt{6}-\sqrt{6}\cdot1}{\sqrt{5}-1}\right):\dfrac{1}{2\sqrt{5}-\sqrt{6}}\)
\(=\left[\dfrac{2\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}+\dfrac{\sqrt{6}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}\right]\cdot\left(2\sqrt{5}-\sqrt{6}\right)\)
\(=\left(2\sqrt{5}+\sqrt{6}\right)\left(2\sqrt{5}-\sqrt{6}\right)\)
\(=\left(2\sqrt{5}\right)^2-\left(\sqrt{6}\right)^2\)
\(=20-6\)
\(=14\)
\(=\left(\dfrac{2\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}+\dfrac{\sqrt{6}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}\right)\cdot\left(2\sqrt{5}-\sqrt{6}\right)\)
\(=\left(2\sqrt{5}+\sqrt{6}\right)\left(2\sqrt{5}-\sqrt{6}\right)\)
=20-6
=14
