\(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) = x + y\(\sqrt{15}\) cross multiply to have: \(\sqrt{3}\) + \(\sqrt{5}\) = x\(\sqrt{5}\) + 5y\(\sqrt{3}\) Collect like roots : x\(\sqrt{5}\) = \(\sqrt{5}\) → x = 1 5y\(\sqrt{3}\) = \(\sqrt{3}\) → y = \(\frac{1}{5}\) ∴ ( x + y ) = 1 + \(\frac{1}{5}\) = 1\(\frac{1}{5}\)