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}=