a \(\left(\sqrt{75}-3\sqrt2-\sqrt{12}\right)\left(\sqrt3+\sqrt2\right)\)
\(=\left(5\sqrt3-2\sqrt3-3\sqrt2\right)\left(\sqrt3+\sqrt2\right)\)
\(=\left(3\sqrt3-3\sqrt2\right)\left(\sqrt3+\sqrt2\right)=3\left(\sqrt3-\sqrt2\right)\left(\sqrt3+\sqrt2\right)\)
\(=3\cdot\left(3-2\right)=3\)
b: \(\frac{3+2\sqrt3}{\sqrt3}+\frac{2+\sqrt2}{\sqrt2+1}-\left(2+\sqrt3\right)\)
\(=\frac{\sqrt3\left(2+\sqrt3\right)}{\sqrt3}+\frac{\sqrt2\left(\sqrt2+1\right)}{\sqrt2+1}-\left(2+\sqrt3\right)\)
\(=2+\sqrt3+\sqrt2-2-\sqrt3=\sqrt2\)
c: \(2\sqrt3\left(\sqrt2-3\right)+\left(\sqrt2-\sqrt3\right)^2+6\sqrt3\)
\(=2\sqrt6-6\sqrt3+5-2\sqrt6+6\sqrt3=5\)
