\(\dfrac{\sqrt{3}-\sqrt{5-2\sqrt{6}}}{\sqrt{3}-\sqrt{2}}-\dfrac{1}{2-\sqrt{3}}\)
\(=\dfrac{\sqrt{3}-\sqrt{\left(\sqrt{2}\right)^2-2\sqrt{3}\cdot\sqrt{2}+\left(\sqrt{3}\right)^2}}{\sqrt{3}-\sqrt{2}}-\dfrac{2+\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\)
\(=\dfrac{\sqrt{3}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}}{\sqrt{3}-\sqrt{2}}-\dfrac{2+\sqrt{3}}{2^2-3}\)
\(=\dfrac{\sqrt{3}+\sqrt{2}-\sqrt{3}}{\sqrt{3}-\sqrt{2}}-\dfrac{2+\sqrt{3}}{4-3}\)
\(=\dfrac{\sqrt{2}\left(\sqrt{3}+\sqrt{2}\right)}{3-2}-\left(2+\sqrt{3}\right)\)
\(=\sqrt{6}+2-2-\sqrt{3}\)
\(=\sqrt{6}-\sqrt{3}\)
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