$\frac{1}{\sqrt{3}+\sqrt{2}}-\sqrt{4-2\sqrt{3}}$
$= \frac{1}{\sqrt{3}+\sqrt{2}} - \sqrt{3-2\sqrt{3}+1}$
$= \frac{1}{\sqrt{3}+\sqrt{2}} - \sqrt{(\sqrt{3}-1)^2}$
$= \frac{1}{\sqrt{3}+\sqrt{2}}- \sqrt{3}+1$
$= \frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})} - \sqrt{3}+1$
$= \sqrt{3}-\sqrt{2}-\sqrt{3}+1$
$= -\sqrt{2}+1$