[tex]a) \ \frac{1}{5+\sqrt{2}} = \frac{1(5-\sqrt{2})}{(5+\sqrt{2})(5-\sqrt{2})} = \frac{5-\sqrt{2}}{25-2} = \frac{5-\sqrt{2}}{23}\\\\\\b) \ \frac{2}{4-\sqrt{3}} = \frac{2(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}=\frac{8+2\sqrt{3}}{16-3} = \frac{8+\sqrt{3}}{13}[/tex]
[tex]c) \ \frac{\sqrt{3}}{\sqrt{5}+\sqrt{3}} = \frac{\sqrt{3}(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})} =\frac{\sqrt{3\cdot5}-\sqrt{3\cdot3}}{5-3} = \frac{\sqrt{15}-3}{2}[/tex]
