#### Answer

$-5 + 2\sqrt 6$

#### Work Step by Step

Simplify. $\dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2+\sqrt3}$
Now, $\dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2+\sqrt3}=\dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2+\sqrt3} \cdot \dfrac{\sqrt 2 -\sqrt 3}{\sqrt 2-\sqrt3}$
or, $=\dfrac{2+3-2\sqrt 2 \sqrt 3}{(\sqrt 2)^2-(\sqrt3)^2}$
or, $=\dfrac{{5 -2\sqrt 6}}{-1}$
we have $=-5 + 2\sqrt 6$