Answer
$\frac{1}{x+1}+\frac{3}{(x+1)^{2}}$
Work Step by Step
The form of the partial fraction decomposition is $\frac{x+4}{(x+1)^{2}}=\frac{A}{x+1}+\frac{B}{(x+1)^{2}}$
This gives $A(x+1)+B= x+4$
Equating the coefficients of x and the constant term, we get A=1, A+B=4 or B=3.
Thus we can write
$\frac{x+4}{(x+1)^{2}}= \frac{1}{x+1}+\frac{3}{(x+1)^{2}}$
