Algebra
# Partial Fractions

Suppose $a$, $b$, and $c$ are constants such that the following holds for all real numbers $x$ such that all of the denominators are nonzero:

$\frac{9}{x(x+1)^2}=\frac{a}{x}+\frac{b}{x+1}+\frac{c}{(x+1)^2}.$ What is the value of $abc?$