a: \(=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)
b: \(=\left(-\sqrt{5}+2\right)\left(\sqrt{5}+2\right)=4-5=-1\)
c: \(=-\sqrt{3}-\sqrt{5}+\sqrt{3}=-\sqrt{5}\)
a.
\(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\dfrac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}=\dfrac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}+\dfrac{2\sqrt{3}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}\)
\(=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)
b.
\(\left(\dfrac{5-2\sqrt{5}}{2-\sqrt{5}}+2\right).\left(\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}+2\right)=\left(\dfrac{-\sqrt{5}\left(2-\sqrt{5}\right)}{2-\sqrt{5}}+2\right)\left(\dfrac{\sqrt{5}\left(3+\sqrt{5}\right)}{3+\sqrt{5}}+2\right)\)
\(=\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)=4-5=-1\)
c.
\(\dfrac{2}{\sqrt{3}-\sqrt{5}}-\dfrac{3-2\sqrt{3}}{2-\sqrt{3}}=\dfrac{2\left(\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}-\sqrt{5}\right)}+\dfrac{\sqrt{3}\left(2-\sqrt{3}\right)}{2-\sqrt{3}}\)
\(=\dfrac{2\left(\sqrt{3}+\sqrt{5}\right)}{-2}+\sqrt{3}=-\sqrt{3}-\sqrt{5}+\sqrt{3}=-\sqrt{5}\)
