Answer
$$B=-2$$
Work Step by Step
$\frac{3x^2+11x+12}{(x+1)(x+3)^2}$ = $\frac{1}{x+1}$-$\frac{B}{x+3}$-$\frac{3}{(x+3)^2}$
Multiplying $(x+1)(x+3)^2$ on both sides:
$3x^2+11x+12 = (x+3)^2-B(x+1)(x+3)-3(x+1)$
Collecting all the $x^2$ terms on both sides of the equation, we have:
$3x^2 = x^2 -Bx^2$
Comparing only the coefficients of the $x^2$ terms:
$3=1-B$ and hence, $B=-2$.
