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

Question

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

Quizplus · Accepted Answer

The correct form for the partial fraction decomposition of the given rational expression involves separating the linear term in the denominator, $x$, and the irreducible quadratic term, $x^2 + 5$. For the linear term, a single constant, $A/x$, is used. For the irreducible quadratic term, a linear expression in the numerator, $Bx + C$, is necessary to account for all possible degrees in the numerator of the original expression.

Write the Form of the Partial Fraction Decomposition of the Rational