Write the form of the partial fraction decomposition of the rational expression. $\frac { 5 x - 1 } { x ^ { 2 } ( x - 7 ) }$
A) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 7 }$
B) $\frac { A } { x ^ { 2 } } + \frac { B } { x + 7 }$
C) $\frac { A } { x ^ { 2 } } + \frac { B x + C } { x + 7 }$
D) $\frac { A x + B } { x } + \frac { C x + D } { x + 7 }$
E) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 7 }$

Question

Write the form of the partial fraction decomposition of the rational expression.  $\frac { 5 x - 1 } { x ^ { 2 } ( x - 7 ) }$  
A) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 7 }$
B) $\frac { A } { x ^ { 2 } } + \frac { B } { x + 7 }$
C) $\frac { A } { x ^ { 2 } } + \frac { B x + C } { x + 7 }$
D) $\frac { A x + B } { x } + \frac { C x + D } { x + 7 }$
E) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 7 }$

Quizplus · Accepted Answer

The rational expression has a quadratic factor $x^2$ and a linear factor $x-7$. The partial fraction decomposition should include terms for each power of the quadratic factor and a term for the linear factor.

Write the Form of the Partial Fraction Decomposition of the Rational