How do you rationalize the denominator and simplify #(5sqrt3-3sqrt2)/(3sqrt2-2sqrt3)#?
Rewrite this as follows
Multiply denominator and nominator with
Multiply the numerator & denominator by the conjugate of the denominator.
Anytime you have "square root plus something" in the denominator, you multiply both num & denom by it's conjugate, i.e. change the sign in the middle.
So the new denominator is
The new numerator is
which (after FOIL) is
So over the new denominator we have