Do I need to use partial fractions to find $\frac{2n+1}{n^2(n+1)^2} = \frac{1}{n^2}-\frac{1}{(n+1)^2}$? I need to simplify $\frac{2n+1}{n^2(n+1^2)}$ as part of an exam question. The solution states $$\frac{2n+1}{n^2(n+1)^2} = \frac{1}{n^2}-\frac{1}{(n+1)^2}$$ 
In the solution it does not state how this simplification was made, I figured this could be done in quite a long winded fashion, using partial fractions. But from how it's written in the solutions it seems like this should be an easy simplification.
Is there a simple trick to simplifying fractions like this?

HINT
Use Partial Fraction Decomposition,
$$\frac{2n+1}{n^2(n+1)^2}=\frac An+\frac B{n^2}+\frac C{n+1}+\frac D{(n+1)^2}$$
$$\iff2n+1=An(n+1)^2+B(n+1)^2+Cn^2(n+1)+Dn^2$$
Now compare the constants & the coefficients of $n,n^2,n^3$ to find $A,B,C,D$

Alternatively by observation,
$$\frac{2n+1}{n^2(n+1)^2}=\frac{(n+1)^2-n^2}{(n+1)^2n^2}=\cdots$$
