$\frac{2a^{-2}}{3 - a^{-2}} - \frac{2a^{-2}}{3 + a^{-2}} = \frac{1}{2} = \frac{2a^{-2}(3 + a^{-2}) - 2a^{-2}(3 - a^{-2})}{(3 - a^{-2})(3 + a^{-2})} = \frac{6a^{-2} + 2a^{-4} - 6a^{-2} + 2a^{-4}}{9 - a^{-4}} = \frac{4a^{-4}}{9 - a^{-4}} = \frac{4\frac{1}{a^4}}{9 - \frac{1}{a^4}} = \frac{\frac{4}{a^4}}{\frac{9a^4 - 1}{a^4}} = \frac{4}{a^4} : \frac{9a^4 - 1}{a^4} = \frac{4}{a^4} * \frac{a^4}{9a^4 - 1} = \frac{4}{9a^4 - 1}$
при $a = (\frac{1}{2})^{-1} = 2^1 = 2$:
$\frac{4}{9a^4 - 1} = \frac{4}{9 * 2^4 - 1} = \frac{4}{9 * 16 - 1} = \frac{4}{144 - 1} = \frac{4}{143}$

$\frac{2a^{-2}}{1 - a^{-2}} + \frac{2a^{-2}}{1 + a^{-2}} = \frac{2a^{-2}(1 + a^{-2}) + 2a^{-2}(1 - a^{-2})}{(1 - a^{-2})(1 + a^{-2})} = \frac{2a^{-2} + 2a^{-4} + 2a^{-2} - 2a^{-4}}{1 - a^{-4}} = \frac{4a^{-2}}{1 - a^{-4}} = \frac{4\frac{1}{a^2}}{1 - \frac{1}{a^4}} = \frac{\frac{4}{a^2}}{\frac{a^4 - 1}{a^4}} = \frac{4}{a^2} : \frac{a^4 - 1}{a^4} = \frac{4}{a^2} * \frac{a^4}{a^4 - 1} = \frac{4a^2}{a^4 - 1}$
при $a = (\frac{1}{5})^{-1} = 5^1 = 5$:
$\frac{4a^2}{a^4 - 1} = \frac{4 * 5^2}{5^4 - 1} = \frac{4 * 25}{625 - 1} = \frac{100}{624} = \frac{25}{156}$

$(\frac{a^{-2}}{2 - a^{-2}})^{-2} - \frac{a^{-2}}{2 + a^{-2}}^{-2} = (\frac{2 - a^{-2}}{a^{-2}})^2 - (\frac{2 + a^{-2}}{a^{-2}}) = \frac{4 - 4a^{-2} + a^{-4}}{a^{-4}} - \frac{4 + 4a^{-2} + a^{-4}}{a^{-4}} = \frac{4 - 4a^{-2} + a^{-4} - 4 - 4a^{-2} - a^{-4}}{a^{-4}} = \frac{-8a^{-2}}{a^{-4}} = -8a^{-2}a^4 = -8a^2$
при $a = (\frac{1}{2})^{-2} = 2^2 = 4$:
$-8a^2 = -8 * 4^2 = -8 * 16 = -128$

$(\frac{2a^{-2}}{5 - a^{-2}})^{-2} - (\frac{2a^{-2}}{5 + a^{-2}})^{-2} = (\frac{5 - a^{-2}}{2a^{-2}})^2 - (\frac{5 + a^{-2}}{2a^{-2}})^2 = \frac{25 - 10a^{-2} + a^{-4}}{4a^{-4}} - \frac{25 + 10a^{-2} + a^{-4}}{4a^{-4}} = \frac{25 - 10a^{-2} + a^{-4} - 25 - 10a^{-2} - a^{-4}}{4a^{-4}} = \frac{-20a^{-2}}{4a^{-4}} = -5a^{-2}a^4 = -5a^2$
при $a = (\frac{1}{2})^{-2} = 2^2 = 4$:
$-5a^2 = -5 * 4^2 = -5 * 16 = -80$