# partial fraction decomposition special case

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.

• Hint: $(r+1)^2 - r^2 = 2r + 1$
• 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 $D$. Dec 29 '17 at 14:43
$$\frac{2r+1}{r^2(r+1)^2}=\frac{(r+1)^2 - r^2}{r^2(r+1)^2} = \frac{1}{r^2} - \frac{1}{(r+1)^2}$$