[tex]\it \dfrac{2(\sqrt6\cdot\sqrt2)}{\sqrt6+\sqrt2}=\dfrac{2\sqrt{12}}{\sqrt6+\sqrt2}=\dfrac{2\sqrt{4\cdot3}}{\sqrt6+\sqrt2}=\dfrac{^{\sqrt6-\sqrt2)}4\sqrt3}{\ \ \ \sqrt6+\sqrt2}=\dfrac{4\sqrt3(\sqrt6-\sqrt2)}{(\sqrt6)^2-(\sqrt2)^2}=\\ \\ \\ =\dfrac{4(\sqrt{18}-\sqrt6)}{6-2}=\dfrac{\not4(\sqrt{9\cdot2}-\sqrt6)}{\not4}=3\sqrt2-\sqrt6[/tex]
