Why do partial fractions sometimes switch the sign? – math.stackexchange.com

Why do partial fractions sometimes switch the sign? – math.stackexchange.com

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According to my solution manual this a valid partial decomposition: $$\frac1{(x^2-1)^2}=\frac A{x-1}+\frac B{(x-1)^2}+\frac C{x+1}+\frac D{(x+1)^2}$$ I'm not sure how I was supposed to know to flip ...

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