# How do you rationalize the denominator and simplify [2sqrt(5) - 3sqrt(2)] / [2sqrt(5) + 3sqrt(2)]?

$19 - 3 \sqrt{10}$
Multiply both numerator and denominator by $\left(2 \sqrt{5} - 3 \sqrt{2}\right)$
$\left[\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} + 3 \sqrt{2}}\right] \left[\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} - 3 \sqrt{2}}\right] = {\left(2 \sqrt{5} - 3 \sqrt{2}\right)}^{2} / \left(20 - 18\right) = \frac{20 + 18 - 6 \sqrt{10}}{2} =$
$= 19 - 3 \sqrt{10}$