\(\dfrac{1}{\sqrt{3}+\sqrt{2}}-\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}\)
\(=\dfrac{\sqrt{3}-\sqrt{2}}{3-2}-\dfrac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}\)
\(=\sqrt{3}-\sqrt{2}-\sqrt{3}=-\sqrt{2}\)
\(\dfrac{1}{\sqrt{3}+\sqrt{2}}-\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}\)
\(=\dfrac{\sqrt{3}-\sqrt{2}}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}-\dfrac{\sqrt{3}\left(\sqrt{5}-\sqrt{4}\right)}{\sqrt{5}-2}\)
\(=\dfrac{\sqrt{3}-\sqrt{2}}{\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2}-\dfrac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}\)
\(=\dfrac{\sqrt{3}-\sqrt{2}}{3-2}-\sqrt{3}\)
\(=\sqrt{3}-\sqrt{2}-\sqrt{3}\)
\(=-\sqrt{2}\)
