# How do you rationalize the denominator and simplify (2sqrt 2-2sqrt 3 )/sqrt3 ?

Multiply both top and bottom of the fraction by $\sqrt{3}$ to remove the irrational denominator.
$\frac{2 \sqrt{2} - 2 \sqrt{3}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{2 \sqrt{2} \sqrt{3} - 2 \left(3\right)}{3} = \frac{2 \sqrt{5} - 6}{3}$