# How do you rationalize the denominator and simplify (3 + sqrt(3) )/ (4-2sqrt(3))?

Mar 21, 2017

$\frac{9 + 5 \sqrt{3}}{2}$

#### Explanation:

You would multiply each term of the fraction by $4 + 2 \sqrt{3}$:

((3+sqrt3)(4+2sqrt3))/((4-2sqrt3)(4+2sqrt3)

$\frac{12 + 6 \sqrt{3} + 4 \sqrt{3} + 6}{16 - 12}$

$\frac{18 + 10 \sqrt{3}}{4}$

$\frac{9 + 5 \sqrt{3}}{2}$