[tex]\frac{\sqrt{10}+5\sqrt{3}}{\sqrt{15}+\sqrt{5}}-\frac{3}{2\sqrt{2}-\sqrt{5}}+\sqrt{9+4\sqrt{2}}[/tex]
[tex]= \frac{\sqrt{5}(\sqrt{2}+\sqrt{15})}{\sqrt{5}(\sqrt{3}+1)}-2\sqrt{2}+\sqrt{5}+2\sqrt{2}+1=\frac{\sqrt{2}+\sqrt{15}}{\sqrt{3}+1}+\sqrt{5}+1=\frac{\sqrt{2}+2\sqrt{15}+\sqrt{3}+\sqrt{5}+1}{\sqrt{3}+1}[/tex] [tex]=\frac{\sqrt{6}-\sqrt{2}-\sqrt{15}+5\sqrt{5}+2}{2}[/tex]