# How do you rationalize the denominator and simplify (sqrt2+sqrt3)/(2sqrt2-3sqrt3)?

$- \frac{13 + 5 \sqrt{6}}{19}$
Multiply both numerator and denominator by the conjugate $\left(2 \sqrt{2} + 3 \sqrt{3}\right)$ of the denominator and use $\left(a - b\right) \left(a + b\right) = \left({a}^{2} - {b}^{2}\right)$
Denominator is rationalized to $\left(- 19\right)$.