# How do you rationalize the denominator and simplify (3sqrt5 )/( 4sqrt3 - 5sqrt2)?

Jul 30, 2016

$- \frac{3}{2} \sqrt{5} \left(4 \sqrt{3} + 5 \sqrt{2}\right)$

#### Explanation:

Since

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$,

you can multiply numerator and denominator of the fraction by the same expression

$\left(4 \sqrt{3} + 5 \sqrt{2}\right)$

to have:

$\frac{3 \sqrt{5} \left(4 \sqrt{3} + 5 \sqrt{2}\right)}{\left(4 \sqrt{3} - 5 \sqrt{2}\right) \left(4 \sqrt{3} + 5 \sqrt{2}\right)} =$

$\frac{3 \sqrt{5} \left(4 \sqrt{3} + 5 \sqrt{2}\right)}{48 - 50} =$

$- \frac{3}{2} \sqrt{5} \left(4 \sqrt{3} + 5 \sqrt{2}\right)$