Ta có: \(\left(\frac{2}{\sqrt{3}-1}+\frac{3}{\sqrt{3}-2}+\frac{15}{3-\sqrt{3}}\right)\cdot\frac{1}{\sqrt{3}+5}\)
\(=\left(\frac{2\sqrt{3}\left(\sqrt{3}-2\right)}{\sqrt{3}\cdot\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)}+\frac{3\cdot\left(3-\sqrt{3}\right)}{\sqrt{3}\cdot\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)}+\frac{15\cdot\left(\sqrt{3}-2\right)}{\sqrt{3}\cdot\left(\sqrt{3}-1\right)\cdot\left(\sqrt{3}-2\right)}\right)\cdot\frac{1}{\sqrt{3}+5}\)
\(=\frac{6-4\sqrt{3}+9-3\sqrt{3}+15\sqrt{3}-30}{\sqrt{3}\cdot\left(\sqrt{3}-1\right)\cdot\left(\sqrt{3}-2\right)}\cdot\frac{1}{\sqrt{3}+5}\)
\(=\frac{\sqrt{3}\left(-5\sqrt{3}+8\right)}{\sqrt{3}\cdot\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)\left(\sqrt{3}+5\right)}\)
\(=\frac{8-5\sqrt{3}}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)\left(\sqrt{3}+5\right)}\)