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This answer gives a really great explanation of why partial fraction decomposition works. However, the explanation implies that rational functions can be decomposed into a sum of fractions plus a polynomial. Yet, when decomposing rational functions we don't seem to account for the potential polynomial term. Why?

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  • $\begingroup$ @TedShifrin Of course, totally forgot about that. Could you please post your comment as an answer? $\endgroup$ – dfg Aug 25 '14 at 3:03
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Sure we do, if the degree of the numerator is at least the degree of the denominator. We do long division first to recover the polynomial part.

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  • $\begingroup$ Great, thanks a lot! $\endgroup$ – dfg Aug 25 '14 at 3:30

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