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