a) \(\frac{\left(\sqrt{3}-\sqrt{5}\right)^2+4\sqrt{15}}{\sqrt{3}+\sqrt{5}}-\sqrt{5}\)
= \(\frac{3-2\sqrt{15}+5+4\sqrt{15}}{\sqrt{3}+\sqrt{5}}-\sqrt{5}\)
=\(\frac{8+2\sqrt{15}-\sqrt{5}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{3}+\sqrt{5}}\)
= \(\frac{8+2\sqrt{15}-\sqrt{15}-\sqrt{25}}{\sqrt{3}+\sqrt{5}}\)
= \(\frac{3+\sqrt{15}}{\sqrt{3}+\sqrt{5}}\)
= \(\frac{\sqrt{3}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{3}+\sqrt{5}}\)
= \(\sqrt{3}\)
b) \(\frac{\left(\sqrt{2}+1\right)^2-4\sqrt{2}}{\sqrt{2}-1}.\left(\sqrt{2}+1\right)\)
= \(\frac{2+2\sqrt{2}+1-4\sqrt{2}}{\sqrt{2}-1}.\left(\sqrt{2}+1\right)\)
= \(\frac{\left(\sqrt{2}-1\right)^2.\left(\sqrt{2}+1\right)}{\sqrt{2}-1}\)
= \(\left(\sqrt{2}-1\right).\left(\sqrt{2}+1\right)\)
= 2 - 1
= 1
