# How do you rationalize the denominator and simplify 3/(2-sqrt2)?

Sep 25, 2015

$\frac{6 + 3 \sqrt{2}}{2}$

#### Explanation:

Rationalize the denominator with the factor $\left(2 + \sqrt{2}\right)$

Hence: $\frac{3}{2 - \sqrt{2}}$ = 3((2 + sqrt(2)))/((2-sqrt2)(2+sqrt(2))

=$3 \frac{\left(2 + \sqrt{2}\right)}{4 + 2 \sqrt{2} - 2 \sqrt{2} - 2}$

= $\frac{6 + 3 \sqrt{2}}{2}$