Answer
$\frac{-6\sqrt 5-2\sqrt 6}{13}$
Work Step by Step
To rationalize the denominator, we multiply both the numerator and the denominator of the expression by $3\sqrt 5+\sqrt 6$ and then simplify:
$\frac{-6}{3\sqrt 5-\sqrt 6}\times\frac{3\sqrt 5+\sqrt 6}{3\sqrt 5+\sqrt 6}$
=$\frac{-6(3\sqrt 5+\sqrt 6)}{(3\sqrt 5-\sqrt 6)(3\sqrt 5+\sqrt 6)}$
=$\frac{-18\sqrt 5-6\sqrt 6}{(3\sqrt 5)^{2}-(\sqrt 6)^{2}}$
=$\frac{-18\sqrt 5-6\sqrt 6}{9(5)-6}$
=$\frac{-18\sqrt 5-6\sqrt 6}{45-6}$
=$\frac{3(-6\sqrt 5-2\sqrt 6)}{39}$
=$\frac{-6\sqrt 5-2\sqrt 6}{13}$
