Prove that a-1a-1+b-1+a-1a-1+b-1=2b2b2-a2.

Prove that $\frac{a^{- 1}}{a^{- 1} + b^{- 1}} + \frac{a^{- 1}}{a^{- 1} + b^{- 1}} = \frac{2 b^{2}}{b^{2} - a^{2}}$ .

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