Question

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

Answer 1

`- ( 13 + 5sqrt6 )/19`

Explanation:

Multiply both numerator and denominator by the conjugate `( 2sqrt2 + 3sqrt3 )` of the denominator and use `( a - b )( a + b ) = (a^2 - b^2 )`
Denominator is rationalized to `(-19)`.