Найдите значение выражения: \(\frac{\sqrt{20}}{5\sqrt{5}+\sqrt{75}}+\frac{\sqrt{12}}{\sqrt{125}+5\sqrt{3}}\).

Упростим корни: \(\sqrt{20}=2\sqrt{5}\), \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{125}=5\sqrt{5}\).

\[\frac{2\sqrt{5}}{5\sqrt{5}+5\sqrt{3}}+\frac{2\sqrt{3}}{5\sqrt{5}+5\sqrt{3}}=\frac{2\sqrt{5}+2\sqrt{3}}{5(\sqrt{5}+\sqrt{3})}.\]

\[\frac{2(\sqrt{5}+\sqrt{3})}{5(\sqrt{5}+\sqrt{3})}=\frac{2}{5}.\]

Ответ: \(\frac{2}{5}\)