Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
$$\frac { x + 9 } { x \left( x ^ { 2 } + 3 \right) ^ { 2 } }$$
A) $\frac { A x + B } { x ^ { 2 } + 3 } + \frac { C x + D } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
B) $\frac { A } { x } + \frac { B } { x ^ { 2 } + 3 } + \frac { C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
C) $\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
D) $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 3 } + \frac { E x + F } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
E) $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 3 } + \frac { D x + E } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The decomposition involves a linear term for the simple root $x$ and linear numerators for the irreducible quadratic factors $x^2 + 3$ and $(x^2 + 3)^2$.

Write the Form of the Partial Fraction Decomposition of the Rational