Given that \(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) 

= x + y\(\sqrt{15}\), find the value of (x + y) 

A.

1\(\frac{3}{5}\)

B.

1\(\frac{2}{5}\)

C.

1\(\frac{1}{5}\)

D.

\(\frac{1}{5}\)

Correct answer is C

\(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\)  = 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\(\frac{1}{5}\)