Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$
A) $\frac { A } { x ^ { 2 } } + \frac { B } { x + 6 }$
B) $\frac { A } { x } + \frac { B x } { x + 6 }$
C) $\frac { A } { x } - \frac { B x } { x + 6 }$
D) $\frac { A } { x } + \frac { B } { x + 6 }$
E) $\frac { A } { x ^ { 2 } } + \frac { B x } { x + 6 }$

Question

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$
A)  $\frac { A } { x ^ { 2 } } + \frac { B } { x + 6 }$
B)  $\frac { A } { x } + \frac { B x } { x + 6 }$
C)  $\frac { A } { x } - \frac { B x } { x + 6 }$
D)  $\frac { A } { x } + \frac { B } { x + 6 }$
E)  $\frac { A } { x ^ { 2 } } + \frac { B x } { x + 6 }$

Quizplus · Accepted Answer

The given expression can be factored as $\frac{1}{x(x+6)}$, which suggests a decomposition into simpler fractions where the denominators are the factors of the original denominator. Thus, the correct form is $\frac{A}{x} + \frac{B}{x+6}$.

Write the Form of the Partial Fraction Decomposition of the Rational