Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $$\frac { 5 x - 4 } { x ^ { 3 } + 5 x }$$
A) $\frac { A } { 5 x - 4 } + \frac { B x + C } { x ^ { 3 } + 5 x }$
B) $\frac { A } { x } - \frac { B x + C } { x ^ { 2 } + 5 } + \frac { D } { x ^ { 3 } + 5 }$
C) $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 5 }$
D) $\frac { A } { x } + \frac { B x - C } { x ^ { 2 } + 5 } + \frac { D } { 5 x - 4 }$
E) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { B x + C } { x + 5 }$

Question

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { 5 x - 4 } { x ^ { 3 } + 5 x }$$ ​
A) $\frac { A } { 5 x - 4 } + \frac { B x + C } { x ^ { 3 } + 5 x }$
B) $\frac { A } { x } - \frac { B x + C } { x ^ { 2 } + 5 } + \frac { D } { x ^ { 3 } + 5 }$
C) $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 5 }$
D) $\frac { A } { x } + \frac { B x - C } { x ^ { 2 } + 5 } + \frac { D } { 5 x - 4 }$
E) $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { B x + C } { x + 5 }$

Quizplus · Accepted Answer

The form of the partial fraction decomposition is determined by the degree of the denominator and the number of distinct linear factors. Since the denominator has a single linear factor (x + 4), the form of the partial fraction decomposition will be of the form A/(x + 4), where A is a constant. The correct choice is C, which has the correct denominators of (x + 4) and (x^2 + 3x + 2), but leaves the constants as unknowns.

Write the Form of the Partial Fraction Decomposition of the Rational