Question

a^-1/a^-1+b^-1 + a^-1/a^-1-b^-1 = -(2b^2)/a^2-b^2​

Answer 1

$we \: will \: reciprocal \: it \: first \\ \frac{a + b}{a} + \frac{a - b}{a} = \frac{ {a}^{2} - {b}^{2} }{ - 2 {b}^{2} } \\ \frac{a + b + a - b}{a} = \frac{(a + b)(a - b)}{ - 2b ^{2} } \\ \frac{2a}{a} = \frac{(a + b)(a - b)}{ - 2b ^{2} } \\ - 2 {b}^{2} a = {(a + b)(a - b)}$

this is your answer and it can't be further solved