\(\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}\)
\(=\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{\sqrt{3}\left(\sqrt{5}-\sqrt{4}\right)}{\sqrt{5}-2}\)
\(=\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}\)
\(=\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{\sqrt{3}}{1}\)
\(=\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{\sqrt{3}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}\)
\(=\frac{1-\sqrt{3}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}\)
\(=\frac{1-3-\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
\(=\frac{-2-\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
\(=\frac{-\sqrt{2}\left(\sqrt{2}+\sqrt{3}\right)}{\sqrt{3}+\sqrt{2}}\)
\(=-\sqrt{2}\)
