Question

Rationalize the denominator. Assume all expressions under radicals represent positive numbers.
frac {sqrt x - sqrt y}{sqrtx + sqrt y}

Answer 1

\[\frac {\sqrt x - \sqrt y}{\sqrt x + \sqrt y}\]

Answer 2

Multiply by the conjugate
\[\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}*\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}} = \frac{x-2\sqrt{x}\sqrt{y}+y}{x-y}\]