a) A\(=\dfrac{2}{3}\sqrt{45}+\dfrac{\sqrt{42}}{\sqrt{21}}-20\sqrt{\dfrac{1}{5}}+\sqrt{10}.\sqrt{2}\)
\(=2\sqrt{5}+\sqrt{2}-4\sqrt{5}+2\sqrt{5}\)
\(=\sqrt{2}\)
b) A\(_2\)\(=\dfrac{\sqrt{10}+\sqrt{5}}{\sqrt{2}+1}+\dfrac{3\sqrt{5}-5}{\sqrt{5}-3}+\dfrac{3}{\sqrt{3}}\)
\(=\dfrac{\sqrt{5}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-\dfrac{\sqrt{5}\left(\sqrt{5}-3\right)}{\sqrt{5}-3}+\dfrac{3}{\sqrt{3}}\)
\(=\sqrt{5}-\sqrt{5}+\sqrt{3}\)
\(=\sqrt{3}\)
c) A\(_3\)\(=\dfrac{1}{\sqrt{3}-2}-\dfrac{2}{\sqrt{5}+\sqrt{3}}+\dfrac{1}{\sqrt{5}+2}\)
\(=\dfrac{\sqrt{3}+2}{-1}-\dfrac{2\left(\sqrt{5}-\sqrt{3}\right)}{2}+\dfrac{\sqrt{5}-2}{1}\)
\(=-\sqrt{3}-2-\sqrt{5}+\sqrt{3}+\sqrt{5}-2\)
\(=-4\)
