( 12^{\frac{1}{2}} - 3^{-\frac{1}{2}})^{-2}=
=[\sqrt{12}-(\frac{1}{3})^{\frac{1}{2}}]^{-2}
=(\sqrt{4 \cdot 3}-\sqrt{\frac{1}{3}})^{-2}
=(2\sqrt3-\frac{1}{\sqrt3})^{-2}
=(\frac{2 \cdot 3 -1}{\sqrt3})^{-2}
=(\frac{5}{\sqrt3})^{-2}
=(\frac{\sqrt3}{5})^2
=\frac{3}{25}