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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1Hint: $(r+1)^2 - r^2 = 2r + 1$ – Rick Dec 29 '17 at 14:41
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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 $D$. – Arthur Dec 29 '17 at 14:43
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Thank you very much, this is clear now. – mysterium Dec 30 '17 at 02:03
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$$\frac{2r+1}{r^2(r+1)^2}=\frac{(r+1)^2 - r^2}{r^2(r+1)^2} = \frac{1}{r^2} - \frac{1}{(r+1)^2}$$
Rick
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