The first step is to rationalize the denominator by multiplying the fraction by the appropriate form of 11:
(3sqrt(3))/(-2 + sqrt(6)) xx (-2 - sqrt(6))/(-2 - sqrt(6)) =>3√3−2+√6×−2−√6−2−√6⇒
(3sqrt(3)(-2 - sqrt(6)))/((-2)^2 + (-2 * -sqrt(6)) + (-2 * sqrt(6)) - (sqrt(6))^2) =>3√3(−2−√6)(−2)2+(−2⋅−√6)+(−2⋅√6)−(√6)2⇒
((-2 * 3sqrt(3)) - (sqrt(6) * 3sqrt(3)))/(4 + 0 - 6) =>(−2⋅3√3)−(√6⋅3√3)4+0−6⇒
(-6sqrt(3) - 3sqrt(6 * 3))/(-2) =>−6√3−3√6⋅3−2⇒
(-6sqrt(3))/(-2) - (3sqrt(18))/(-2) =>−6√3−2−3√18−2⇒
3sqrt(3) + (3sqrt(9 * 2))/2 =>3√3+3√9⋅22⇒
3sqrt(3) + (3sqrt(9)sqrt(2))/2 =>3√3+3√9√22⇒
3sqrt(3) + (3 * 3sqrt(2))/2 =>3√3+3⋅3√22⇒
3sqrt(3) + (9sqrt(2))/23√3+9√22
