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 involves breaking it down into simpler fractions. Since the denominator is $x(x-4)$, the decomposition will involve terms of the form $\frac{A}{x}$ and $\frac{B}{x-4}$, where A and B are constants to be determined. This matches option E.

Write the Form of the Partial Fraction Decomposition of the Rational