Factor $20=2^{2}\times 5$. Rewrite the square root of the product $\sqrt{2^{2}\times 5}$ as the product of square roots $\sqrt{2^{2}}\sqrt{5}$. Take the square root of $2^{2}$.
$$\frac{\sqrt{3}+\sqrt{5}}{3\times 2\sqrt{5}}$$
Multiply $3$ and $2$ to get $6$.
$$\frac{\sqrt{3}+\sqrt{5}}{6\sqrt{5}}$$
Rationalize the denominator of $\frac{\sqrt{3}+\sqrt{5}}{6\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.
