d: \(\frac{3+2\sqrt3}{\sqrt3}+\frac{2+\sqrt2}{\sqrt2+1}-\left(2+\sqrt3\right)\)
\(=2+\sqrt3+\frac{\sqrt2\left(\sqrt2+1\right)}{\sqrt2+1}-2-\sqrt3\)
\(=\sqrt2\)
e: \(\frac{\sqrt{10}-\sqrt6}{\sqrt5-\sqrt3}-\frac{4}{\sqrt2-1}+\frac{6}{\sqrt2}\)
\(=\frac{\sqrt2\left(\sqrt5-\sqrt3\right)}{\sqrt5-\sqrt3}-\frac{4\left(\sqrt2+1\right)}{\left(\sqrt2+1\right)\left(\sqrt2-1\right)}+3\sqrt2\)
\(=\sqrt2+3\sqrt2-4\left(\sqrt2+1\right)=4\sqrt2-4\sqrt2-4=-4\)
f: \(\frac{6-\sqrt{12}}{\sqrt{24}-\sqrt8}-\frac{3+\sqrt3}{\sqrt3}+\frac{4}{1-\sqrt3}\)
\(=\frac{6-2\sqrt3}{\sqrt8\left(\sqrt3-1\right)}-\sqrt3-1-\frac{4}{\sqrt3-1}\)
\(=\frac{2\sqrt3\left(\sqrt3-1\right)}{2\sqrt2\left(\sqrt3-1\right)}-\sqrt3-1-\frac{4\left(\sqrt3+1\right)}{\left(\sqrt3+1\right)\left(\sqrt3-1\right)}\)
\(=\frac{\sqrt3}{\sqrt2}-\sqrt3-1-2\left(\sqrt3+1\right)=\frac{\sqrt6}{2}-\sqrt3-1-2\sqrt3-2=\frac{\sqrt6}{2}-3\sqrt3-3\)
