a) \(\dfrac{5-2\sqrt{5}}{\sqrt{5}}+\dfrac{20}{5+\sqrt{5}}\)
\(=\dfrac{\left(5-2\sqrt{5}\right)\sqrt{5}}{\sqrt{5}}+\dfrac{20}{5+\sqrt{5}}\)
\(=\dfrac{\left(5-2\sqrt{5}\right)\sqrt{5}}{5}+\dfrac{20\left(5-\sqrt{5}\right)}{20}\)
\(=\dfrac{5\sqrt{5}-10}{5}+5-\sqrt{5}\)
\(=\dfrac{5\left(\sqrt{5}-2\right)}{5}+5-\sqrt{5}\)
\(=\sqrt{5}-2+5-\sqrt{5}\)
\(=\left(\sqrt{5}-\sqrt{5}\right)+\left(-2+5\right)\)
\(=0+\left(-2+5\right)\)
\(=3\)
b) \(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2}}-\left(\sqrt{3}+\sqrt{2}\right)\)
\(=\dfrac{\left(3+2\sqrt{3}\right)\sqrt{3}}{3}+\dfrac{\left(2+\sqrt{2}\right)\sqrt{2}}{2}-\sqrt{3}-\sqrt{2}\)
\(=\dfrac{3\sqrt{3}+6}{3}+\dfrac{2\sqrt{2}+2}{2}-\sqrt{3}-\sqrt{2}\)
\(=\dfrac{3\left(\sqrt{3}+2\right)}{3}+\dfrac{2\left(\sqrt{2}+1\right)}{2}-\sqrt{3}-\sqrt{2}\)
\(=\sqrt{3}+2+\sqrt{2}+1-\sqrt{3}-\sqrt{2}\)
\(=\left(\sqrt{3}-\sqrt{3}\right)+\left(\sqrt{2}-\sqrt{2}\right)+\left(2+1\right)\)
\(=3\)
