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i'm trying to understand, how WolframAlpha solves an quite difficult Integral, however i don't know what wolframAlpha is doing in this step:

1 / ((p-1) * p) --> ((1/(p-1)) - (1/p)) 

Everything i could think of is --> ((1/(p-1)) * (1/p))

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Thanks for your help :)

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    I'm unreasonably bothered by the fact that the alt-text is captured in that image.2011-11-09

1 Answers 1

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It is performing the partial fraction decomposition. You can check that result is correct by recombining fractions like so: $\frac{1}{p-1} - \frac{1}{p} = \frac{p}{p (p-1)} - \frac{p-1}{p(p-1)} = \frac{p -(p-1)}{p (p-1)} = \frac{1}{p(p-1)}$ (credit-waived; above is a verbatim copy of another user's now deleted answer).