We have (I believe):
(3sqrt2-2sqrt3)/(sqrt2+sqrt3)3√2−2√3√2+√3
I'm going to first work with the denominator and rationalize it:
(3sqrt2-2sqrt3)/(sqrt2+sqrt3)xx(sqrt2-sqrt3)/(sqrt2-sqrt3)3√2−2√3√2+√3×√2−√3√2−√3
((3sqrt2-2sqrt3)(sqrt2-sqrt3))/((sqrt2+sqrt3)(sqrt2-sqrt3))(3√2−2√3)(√2−√3)(√2+√3)(√2−√3)
(3sqrt2sqrt2-3sqrt2sqrt3-2sqrt3sqrt2+2sqrt3sqrt3)/(sqrt2sqrt2-sqrt2sqrt3+sqrt2sqrt3+sqrt3sqrt3)3√2√2−3√2√3−2√3√2+2√3√3√2√2−√2√3+√2√3+√3√3
((3xx2)-3sqrt6-2sqrt6+(2xx3))/(2+3)(3×2)−3√6−2√6+(2×3)2+3
(6-5sqrt6+6)/56−5√6+65
6/5-sqrt665−√6
