a: \(\frac{\sqrt{8-2\sqrt{15}}}{\sqrt3-\sqrt5}-\sqrt{\left(1-3\right)^2}\)
\(=\frac{\sqrt{\left(\sqrt5-\sqrt3\right)^2}}{-\left(\sqrt5-\sqrt3\right)}-\left|1-3\right|\)
\(=\frac{\sqrt5-\sqrt3}{-\left(\sqrt5-\sqrt3\right)}-2=-1-2=-3\)
b: \(3\sqrt{27}-\sqrt{98}-3\sqrt3\)
\(=3\cdot3\sqrt3-3\sqrt3-7\sqrt2\)
\(=9\sqrt3-3\sqrt3-7\sqrt2=6\sqrt3-7\sqrt2\)
c: \(\left(\frac{4}{\sqrt5-1}+\sqrt7\right)\left(\frac{4}{\sqrt5+1}-\sqrt7\right)\)
\(=\left(\frac{4\left(\sqrt5+1\right)}{\left(\sqrt5+1\right)\left(\sqrt5-1\right)}+\sqrt7\right)\left(\frac{4\left(\sqrt5-1\right)}{\left(\sqrt5+1\right)\left(\sqrt5-1\right)}-\sqrt7\right)\)
\(=\left(\sqrt5+1+\sqrt7\right)\left(\sqrt5-1-\sqrt7\right)\)
\(=5-\left(\sqrt7+1\right)^2=5-8-2\sqrt7=-2\sqrt7-3\)
