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 correct form for partial fraction decomposition of $\frac{5x - 1}{x^2(x - 7)}$ is $\frac{A}{x} + \frac{B}{x^2} + \frac{C}{x - 7}$ because the denominator has a repeated linear factor $x^2$ and a distinct linear factor $x - 7$.

Write the Form of the Partial Fraction Decomposition of the Rational