d: \(\frac{4}{\sqrt3-1}-2\cdot\sqrt{\left(\sqrt3-1\right)^2}\)
\(=\frac{4\left(\sqrt3+1\right)}{\left.\left(\sqrt3-1\right)\left(\sqrt3+1\right)\right.}-2\left(\sqrt3-1\right)\)
\(=2\left(\sqrt3+1\right)-2\left(\sqrt3-1\right)=2\sqrt3+2-2\sqrt3+2=4\)
e: \(5\sqrt{\frac15}-\frac{8}{\sqrt5+1}+\frac{\sqrt{20}-5}{2-\sqrt5}\)
\(=\sqrt5-\frac{8\left(\sqrt5-1\right)}{\left(\sqrt5+1\right)\left(\sqrt5-1\right)}+\frac{\sqrt5\left(2-\sqrt5\right)}{2-\sqrt5}\)
\(=\sqrt5+\sqrt5-2\left(\sqrt5-1\right)=2\sqrt5-2\sqrt5+2=2\)
f: \(\frac{7}{\sqrt{10}-\sqrt3}-\frac{5\sqrt2-2\sqrt5}{\sqrt5-\sqrt2}-\frac{6}{\sqrt3}\)
\(=\frac{7\left(\sqrt{10}+\sqrt3\right)}{\left(\sqrt{10}-\sqrt3\right)\left(\sqrt{10}+\sqrt3\right)}-\frac{\sqrt{10}\left(\sqrt5-\sqrt2\right)}{\sqrt5-\sqrt2}-2\sqrt3\)
\(=\sqrt{10}+\sqrt3-\sqrt{10}-2\sqrt3=-\sqrt3\)
g: \(\frac{3+\sqrt3}{\sqrt3}-\frac{2}{\sqrt3-1}\)
\(=\frac{\sqrt3\left(\sqrt3+1\right)}{\sqrt3}-\frac{2\left(\sqrt3+1\right)}{\left(\sqrt3+1\right)\left(\sqrt3-1\right)}\)
\(=\sqrt3+1-\left(\sqrt3+1\right)=0\)
h: \(\frac{\sqrt{15}-\sqrt5}{\sqrt3-1}+\sqrt{\left(2-\sqrt5\right)^2}-2\sqrt5\)
\(=\frac{\sqrt5\left(\sqrt3-1\right)}{\sqrt3-1}+\sqrt5-2-2\sqrt5\)
\(=\sqrt5-2-\sqrt5=-2\)
