Answer
$\frac{3}{x+3}-\frac{2}{(x+3)^2}$
Work Step by Step
1. Let the decomposition be
$\frac{3x+7}{(x+3)^2}=\frac{A}{x+3}+\frac{B}{(x+3)^2}$
2. Combine the right side to get $\frac{Ax+3A+B}{(x+3)^2}$
3. Thus $A=3$ and $3A+B=7$, thus $B=7-3(3)=2$
4. we have $\frac{3x+7}{(x+3)^2}=\frac{3}{x+3}-\frac{2}{(x+3)^2}$
