# How do you rationalize the denominator and simplify 1/(sqrta+sqrtb)?

Mar 12, 2016

$= \frac{\sqrt{a} - \sqrt{b}}{a - b}$

#### Explanation:

Given:$\text{ } \frac{1}{\sqrt{a} + \sqrt{b}}$

Known:$\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$

So using the above known information multiply by 1 but in the form of $1 = \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$

So
$= \frac{1}{\sqrt{a} - \sqrt{b}} \times \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$

$= \frac{\sqrt{a} - \sqrt{b}}{a - b}$