Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$$\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$$
A) $\frac { 5 } { x - 1 } + \frac { - 5 x + 2 } { x ^ { 2 } + x + 1 }$
B) $\frac { 5 } { x - 1 } + \frac { - 5 } { x + 1 } + \frac { 2 } { x - 1 }$
C) $\frac { - 5 } { x - 1 } + \frac { 5 x + 2 } { x ^ { 2 } + x + 1 }$
D) $\frac { 5 } { x - 1 } + \frac { 2 x - 5 } { x ^ { 2 } + x + 1 }$

Question

Quizplus · Accepted Answer

The quadratic factor $x^2 + x + 1$ is prime and nonrepeated, so the partial fraction decomposition has the form $\frac { A } { x - 1 } + \frac { B x + C } { x ^ { 2 } + x + 1 }$.

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor 12x+3(x−1)(x2+x+1)\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }(x−1)(x2+x+1)12x+3​

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$