The value of $$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} - \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}})$$ is

$$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} - \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}})$$

=$$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} * \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}- {\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2} }x \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}})$$

= $$(\sqrt{5}+\sqrt{3})(\sqrt{15} - \sqrt{6} - \sqrt{15} + \sqrt{10})$$ = $$(\sqrt{5}+\sqrt{3})(\sqrt{10}-\sqrt{6})$$ = $$2\sqrt{2}$$