Answer
$-5+2\sqrt{6}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}
$ results to
\begin{array}{l}
\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}
\cdot
\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}}
\\\\=
\dfrac{(\sqrt{2}-\sqrt{3})^2}{(\sqrt{2})^2-(\sqrt{3})^2}
\\\\=
\dfrac{(\sqrt{2})^2+2(\sqrt{2})(-\sqrt{3})+(-\sqrt{3})^2}{2-3}
\\\\=
\dfrac{2-2\sqrt{6}+3}{-1}
\\\\=
-2+2\sqrt{6}-3
\\\\=
-5+2\sqrt{6}
.\end{array}