Write the Partial Fraction Decomposition of the Rational Expression $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

A) $\frac { 5 } { x - 1 } + \frac { - 5 x + 2 } { x ^ { 2 } + x + 1 }$
B) $\frac { 5 } { x - 1 } + \frac { 2 x - 5 } { x ^ { 2 } + x + 1 }$
C) $\frac { 5 } { x - 1 } + \frac { - 5 } { x + 1 } + \frac { 2 } { x - 1 }$
D) $\frac { - 5 } { x - 1 } + \frac { 5 x + 2 } { x ^ { 2 } + x + 1 }$