# How do you rationalize the denominator and simplify ( 2sqrtx - 3sqrty)/(sqrtx + sqrty)?

Nov 11, 2017

The answer is $= \frac{2 x - 5 \sqrt{x y} + 3 y}{x - y}$

#### Explanation:

Let $p = \frac{2 \sqrt{x} - 3 \sqrt{y}}{\sqrt{x} + \sqrt{y}}$

Multiply the numerator and denominator by $\left(\sqrt{x} - \sqrt{y}\right)$

Therefore,

$p = \frac{\left(2 \sqrt{x} - 3 \sqrt{y}\right) \left(\left(\sqrt{x} - \sqrt{y}\right)\right)}{\left(\sqrt{x} + \sqrt{y}\right) \left(\left(\sqrt{x} - \sqrt{y}\right)\right)}$

$= \frac{2 x - 5 \sqrt{x y} + 3 y}{x - y}$