prove
![\frac{ {a}^{ - 1} }{ {a}^{ - 1} + {b}^{ - 1} } + \frac{ {a}^{ - 1} }{ {a}^{ - 1} - {b}^{ - 1} } = \frac{ - (2 {b}^{2} )}{ {a}^{2} - {b}^{2} } \frac{ {a}^{ - 1} }{ {a}^{ - 1} + {b}^{ - 1} } + \frac{ {a}^{ - 1} }{ {a}^{ - 1} - {b}^{ - 1} } = \frac{ - (2 {b}^{2} )}{ {a}^{2} - {b}^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+%7Ba%7D%5E%7B+-+1%7D+%7D%7B+%7Ba%7D%5E%7B+-+1%7D+%2B++%7Bb%7D%5E%7B+-+1%7D++%7D++%2B++%5Cfrac%7B+%7Ba%7D%5E%7B+-+1%7D+%7D%7B+%7Ba%7D%5E%7B+-+1%7D+-++%7Bb%7D%5E%7B+-+1%7D++%7D++%3D++%5Cfrac%7B+-+%282+%7Bb%7D%5E%7B2%7D+%29%7D%7B+%7Ba%7D%5E%7B2%7D++-++%7Bb%7D%5E%7B2%7D+%7D+)
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