1)
[tex]\frac{2\sqrt6}{\sqrt3-2}*\frac{\sqrt3+2}{\sqrt3+2}=\frac{2\sqrt{18}+4\sqrt6}{3-4}=\frac{2\sqrt{9*2}+4\sqrt6}{-1}}=-6\sqrt2-4\sqrt6[/tex]
2)
[tex]\frac{\sqrt2-1}{2\sqrt2+1}*\frac{2\sqrt2-1}{2\sqrt2-1}=\frac{4-\sqrt2-2\sqrt2+1}{8-1}=\frac{5-3\sqrt2}{7}[/tex]
3)
[tex]\frac{\sqrt3+2}{3-2\sqrt3}*\frac{3+2\sqrt3}{3+2\sqrt3}=\frac{3\sqrt3+6+6+4\sqrt3}{9-12}=\frac{7\sqrt3+12}{-3}=-\frac{7\sqrt3+12}{3}[/tex]
4)
[tex]\frac{\sqrt5-\sqrt3}{2\sqrt3+\sqrt5}*\frac{2\sqrt3-\sqrt5}{2\sqrt3-\sqrt5}=\frac{2\sqrt{15}-5-6+\sqrt{15}}{12-5}=\frac{3\sqrt{15}-11}{7}[/tex]
