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I would like to have the following partial fraction decomposed : $$\frac{2r+1}{r^2{(r+1)}^2}$$ Since the denominator does not contain any constant the approch is non-trivial to me. Any help would be highly appreciated.

Thank you in advance.

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    $\begingroup$ Hint: $(r+1)^2 - r^2 = 2r + 1$ $\endgroup$
    – Rick
    Dec 29 '17 at 14:41
  • $\begingroup$ The approach is the same it always is: write it as $\frac{Ar+B}{r^2}+\frac{Cr+D}{(1+r)^2}$, and solve for $A,B,C$ and $D$. $\endgroup$
    – Arthur
    Dec 29 '17 at 14:43
  • $\begingroup$ Thank you very much, this is clear now. $\endgroup$
    – mysterium
    Dec 30 '17 at 2:03
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$$\frac{2r+1}{r^2(r+1)^2}=\frac{(r+1)^2 - r^2}{r^2(r+1)^2} = \frac{1}{r^2} - \frac{1}{(r+1)^2}$$

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    $\begingroup$ Thanks again, this helped a lot. $\endgroup$
    – mysterium
    Dec 30 '17 at 2:04

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