Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$\frac { x ^ { 2 } + 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
A) $\frac { 1 } { x ^ { 2 } + 3 } + \frac { 4 x - 5 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
B) $\frac { x + 1 } { x ^ { 2 } + 3 } + \frac { 4 x - 5 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
C) $\frac { 1 } { x ^ { 2 } + 3 } + \frac { - x - 5 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
D) $\frac { - 1 } { x ^ { 2 } + 3 } + \frac { 4 x - 5 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The denominator has a repeated quadratic factor, so the partial fraction decomposition will have the form $\frac { A } { x ^ { 2 } + 3 } + \frac { B x + C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$.

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor x2+4x−2(x2+3)2\frac { x ^ { 2 } + 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }(x2+3)2x2+4x−2​

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor $\frac { x ^ { 2 } + 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$