A = \frac{{\sqrt {4 - 2\sqrt 3 } }}{{\sqrt 6 - \sqrt 2 }}= \frac{{\sqrt {(\sqrt 3 - 1)^2 } }}{{\sqrt 2 (\sqrt 3 - 1)}} = \frac{{\sqrt 3 - 1}}{{\sqrt 2 (\sqrt 3- 1)}} = \frac{1}{{\sqrt 2 }} = \frac{{\sqrt 2 }}{2}