\frac{(\sqrt3+3\sqrt5)^2}{(\sqrt3-3\sqrt5)^2}=\frac{3+6\sqrt{15}+9*5}{3-6\sqrt{15}+9*5}=\frac{48+6\sqrt{15}}{48-6\sqrt{15}}=\frac{6(8+\sqrt{15})}{6(8-\sqrt{15})}=
\frac{8+\sqrt{15}}{8-\sqrt{15}}=\frac{(8+\sqrt{15})(8+\sqrt{15})}{(8-\sqrt{15})(8+\sqrt{15})}=\frac{(8+\sqrt{15})^2}{8^2-(\sqrt{15})^2}=\frac{(8+\sqrt{15})^2}{64-15}=
\frac{64+16\sqrt{15}+15}{49}=\frac{79+16\sqrt{15}}{49}