[tex]\boxed{\frac{4\sqrt3}{3+\sqrt7}.\frac{3-\sqrt7}{3-\sqrt7}=\frac{12\sqrt3-4\sqrt{21}}{9-7}=\frac{12\sqrt3-4\sqrt{21}}{2}}[/tex]
[tex]\boxed{\frac{2}{5-\sqrt3}.\frac{5+\sqrt3}{5+\sqrt3}=\frac{10+2\sqrt3}{25-3}=\frac{10+2\sqrt3}{22}}[/tex]
[tex]\boxed{\frac{8}{4-\sqrt{10}}.\frac{4+\sqrt{10}}{4+\sqrt{10}}=\frac{32+8\sqrt{10}}{16-10}=\frac{32+8\sqrt{10}}{6}=\frac{16+4\sqrt{10}}{3}}[/tex]
[tex]\boxed{\frac{4\sqrt3}{\sqrt5+\sqrt2}.\frac{\sqrt5-\sqrt2}{\sqrt5-\sqrt2}=\frac{4\sqrt{15}-4\sqrt6}{3}}[/tex]
