\(\frac{\sqrt{x} + \sqrt{y}}{x - y} = \frac{2\sqrt{x} + 2\sqrt{y}}{x + 2\sqrt{xy} + y}\)

\(\frac{\sqrt{x} + \sqrt{y}}{(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})} = \frac{2(\sqrt{x} + \sqrt{y})}{(\sqrt{x} + \sqrt{y})^2}\)

\(\frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} - \sqrt{y}} = 2\)

Using componendo / dividend

\(\frac{2\sqrt{x}}{\sqrt{x} - \sqrt{y}} = \frac{2+1}{1} = 3\) ....................... (1)

\(\frac{2\sqrt{y}}{\sqrt{x} - \sqrt{y}} = \frac{2-1}{1} = 1\) ........................ (2)

Divide (1) by (2)

\(\frac{\sqrt{x}}{\sqrt{y}} = \frac{3}{1}\)

\(\frac{x}{y} = 9\)

Answer = E

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