Write the form of the partial fraction decomposition of the rational expression. $$\frac { 6 x - 1 } { x ( x - 4 ) }$$
A) $\frac { A x + B } { x } + \frac { C x + D } { x + 4 }$
B) $\frac { A } { x } - \frac { B } { x + 4 }$
C) $\frac { A } { x } + \frac { B x + C } { x + 4 }$
D) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 4 }$
E) $\frac { A } { x } + \frac { B } { x - 4 }$

Question

Write the form of the partial fraction decomposition of the rational expression.​ $$\frac { 6 x - 1 } { x ( x - 4 ) }$$ ​
A) $\frac { A x + B } { x } + \frac { C x + D } { x + 4 }$
B) $\frac { A } { x } - \frac { B } { x + 4 }$
C) $\frac { A } { x } + \frac { B x + C } { x + 4 }$
D) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 4 }$
E) $\frac { A } { x } + \frac { B } { x - 4 }$

Quizplus · Accepted Answer

The correct form for the partial fraction decomposition of the given rational expression $\frac { 6 x - 1 } { x ( x - 4 ) }$ is $\frac { A } { x } + \frac { B } { x - 4 }$, where $A$ and $B$ are constants to be determined. This is because the denominator factors into distinct linear factors, each of which should correspond to a separate term in the decomposition with a constant numerator.

Write the Form of the Partial Fraction Decomposition of the Rational