# How do you evaluate \frac { 7} { 2+ 2\sqrt { 3} }?

Dec 28, 2016

$\frac{7}{2 + 2 \sqrt{3}} = \frac{7 \sqrt{3} - 7}{4}$

#### Explanation:

$\frac{7}{2 + 2 \sqrt{3}} = \frac{7}{2 \sqrt{3} + 2}$

= $\frac{7}{2 \sqrt{3} + 2} \times \frac{2 \sqrt{3} - 2}{2 \sqrt{3} - 2}$ and using $\left(a + b\right) \left(a - b\right) = \left({a}^{2} - {b}^{2}\right)$, we get

$\frac{7 \left(2 \sqrt{3} - 2\right)}{{\left(2 \sqrt{3}\right)}^{2} - {2}^{2}}$

= $\frac{14 \sqrt{3} - 14}{12 - 4}$

= $\frac{14 \sqrt{3} - 14}{8}$ and dividing numerator and denominator by $2$

= $\frac{7 \sqrt{3} - 7}{4}$