Write the Partial Fraction Decomposition of the Improper Rational Expression $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }$

Multiple Choice

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }$

A) $1 + \frac { 4 x - 1 } { x ^ { 2 } + x + 1 }$
B) $1 + \frac { 3 x - 1 } { x ^ { 2 } + x + 1 }$
C) $\frac { x ^ { 2 } } { x ^ { 2 } + x + 1 } + \frac { 4 x } { x ^ { 2 } + x + 1 }$
D) $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }$
E) $\frac { 3 x - 1 } { x ^ { 2 } + x + 1 }$