Question

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

Answer 1

Multiply the numerator and the denominator by the conjugate of the denominator.

`(3sqrt(2)+sqrt(3))/(2sqrt(2)-3sqrt(3)) * (2sqrt(2)+3sqrt(3))/(2sqrt(2)+3sqrt(3))`

`=(21+11sqrt(6))/(8-27)`

`= -(21+11sqrt(6))/19`