Find the partial fraction decomposition.
-$$\frac { - 4 x ^ { 2 } - 33 x - 54 } { x ^ { 3 } + 6 x ^ { 2 } + 9 x }$$
A) $\frac { - 6 } { x } + \frac { - 3 } { ( x + 3 ) ^ { 2 } }$
B) $\frac { - 6 } { x } + \frac { 2 } { x + 3 } + \frac { - 3 x } { ( x + 3 ) ^ { 2 } }$
C) $\frac { - 6 } { x } + \frac { 2 x - 3 } { ( x + 3 ) ^ { 2 } }$
D) $\frac { - 6 } { x } + \frac { 2 } { x + 3 } + \frac { - 3 } { ( x + 3 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The denominator factors as $x(x+3)^2$. The partial fraction decomposition is $\frac{A}{x} + \frac{B}{x+3} + \frac{C}{(x+3)^2}$. Solving for A, B, and C gives the decomposition in choice D.

Find the Partial Fraction Decomposition −4x2−33x−54x3+6x2+9x\frac { - 4 x ^ { 2 } - 33 x - 54 } { x ^ { 3 } + 6 x ^ { 2 } + 9 x }x3+6x2+9x−4x2−33x−54​

Find the Partial Fraction Decomposition $\frac { - 4 x ^ { 2 } - 33 x - 54 } { x ^ { 3 } + 6 x ^ { 2 } + 9 x }$