a: \(A=\frac{1}{\sqrt3-2}-\frac{\sqrt{12}-\sqrt{15}}{\sqrt5-2}\)
\(=\frac{\sqrt3+2}{\left(\sqrt3-2\right)\left(\sqrt3+2\right)}+\frac{\sqrt3\left(\sqrt5-2\right)}{\sqrt5-2}\)
\(=-2-\sqrt3+\sqrt3=-2\)
b: \(B=\frac{1}{\sqrt3-2}-\frac{1}{\sqrt3+2}\)
\(=\frac{\sqrt3+2-\left(\sqrt3-2\right)}{\left(\sqrt3+2\right)\left(\sqrt3-2\right)}\)
\(=\frac{4}{3-4}=\frac{4}{-1}=-4\)
c: \(C=2\cdot\sqrt{4+\sqrt{6-2\sqrt5}}\left(\sqrt{10}-\sqrt2\right)\)
\(=2\cdot\sqrt{4+\sqrt{\left(\sqrt5-1\right)^2}}\cdot\sqrt2\left(\sqrt5-1\right)\)
\(=2\cdot\sqrt{3+\sqrt5}\cdot\sqrt2\cdot\left(\sqrt5-1\right)\)
\(=2\cdot\sqrt{6+2\sqrt5}\cdot\left(\sqrt5-1\right)=2\left(\sqrt5+1\right)\left(\sqrt5-1\right)=2\cdot\left(5-1\right)=2\cdot4=8\)
