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

Question

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

Quizplus · Accepted Answer

The correct partial fraction decomposition of $\frac{1}{x(x+q)}$ is $\frac{1}{q}\left(\frac{1}{x} - \frac{1}{x+q}\right)$, which simplifies to the original expression when combined over a common denominator.

Write the Partial Fraction Decomposition of the Rational Expression 1x(x+q)\frac { 1 } { x ( x + q ) }x(x+q)1​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 1 } { x ( x + q ) }$