Answer
$-5+2\sqrt {6}$
Work Step by Step
$\frac{\sqrt 2-\sqrt 3}{\sqrt 2+\sqrt 3}\times\frac{\sqrt 2-\sqrt 3}{\sqrt 2-\sqrt 3}$
=$\frac{(\sqrt 2-\sqrt 3)(\sqrt 2-\sqrt 3)}{(\sqrt 2-\sqrt 3)(\sqrt 2+\sqrt 3)}$
=$\frac{\sqrt 2(\sqrt 2-\sqrt 3)-\sqrt 3(\sqrt 2-\sqrt 3)}{(\sqrt 2)^{2}-(\sqrt 3)^{2}}$
=$\frac{\sqrt 2\sqrt 2-\sqrt 2\sqrt 3-\sqrt 2\sqrt 3+\sqrt 3\sqrt 3}{2-3}$
=$\frac{2-\sqrt {2\times3}-\sqrt {2\times3}+3}{-1}$
=$\frac{2-\sqrt {6}-\sqrt {6}+3}{-1}$
=$\frac{5-2\sqrt {6}}{-1}$
=$-5+2\sqrt {6}$
