Write the partial fraction decomposition of the rational expression. $\frac { - 3 x ^ { 2 } - 3 x + 27 } { x ^ { 2 } ( x + 3 ) }$
A) $\frac { 1 } { x + 3 } + \frac { 9 } { x ^ { 2 } }$
B) $\frac { 1 } { x + 3 } - \frac { 4 } { x } + \frac { 2 } { x ^ { 2 } }$
C) $\frac { 1 } { x + 3 } - \frac { 4 } { x } + \frac { 9 } { x ^ { 2 } }$
D) $\frac { 1 } { x + 3 } + \frac { 4 } { x } - \frac { 9 } { x ^ { 2 } }$
E) $\frac { - 3 } { x + 3 } - \frac { 3 } { x ( x + 3 ) } + \frac { 27 } { x ^ { 2 } ( x + 3 ) }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition of the given rational expression $\frac { - 3 x ^ { 2 } - 3 x + 27 } { x ^ { 2 } ( x + 3 ) }$ is $\frac { 1 } { x + 3 } - \frac { 4 } { x } + \frac { 9 } { x ^ { 2 } }$. This decomposition correctly separates the expression into parts that correspond to the factors of the denominator.

Write the Partial Fraction Decomposition of the Rational Expression −3x2−3x+27x2(x+3)\frac { - 3 x ^ { 2 } - 3 x + 27 } { x ^ { 2 } ( x + 3 ) }x2(x+3)−3x2−3x+27​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { - 3 x ^ { 2 } - 3 x + 27 } { x ^ { 2 } ( x + 3 ) }$