[tex]\displaystyle\frac{\sqrt{6} +2}{\sqrt{6}-2 }- \frac{\sqrt{6}-2 }{\sqrt{6} +2} =\frac{(\sqrt{6} +2)^2-(\sqrt{6} -2)^2}{(\sqrt{6}-2)(\sqrt{6} +2)} =\frac{6+4\sqrt{6}+4-6+4\sqrt{6} -4 }{6-4} =\\\\=\frac{8\sqrt{6} }{2} =4\sqrt{6}}[/tex]