Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 } { x ^ { 2 } + 5 x }$
A) $\frac { A } { x } + \frac { B } { x - 5 }$
B) $\frac { 1 } { x } - \frac { 1 } { x + 5 }$
C) $\frac { 1 } { x } + \frac { 1 } { x + 5 }$
D) $\frac { A } { x } - \frac { B } { x - 5 }$
E) $\frac { 1 } { x } - \frac { 1 } { x - 5 }$

Question

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  $\frac { 5 } { x ^ { 2 } + 5 x }$  
A) $\frac { A } { x } + \frac { B } { x - 5 }$
B) $\frac { 1 } { x } - \frac { 1 } { x + 5 }$
C) $\frac { 1 } { x } + \frac { 1 } { x + 5 }$
D) $\frac { A } { x } - \frac { B } { x - 5 }$
E) $\frac { 1 } { x } - \frac { 1 } { x - 5 }$

Quizplus · Accepted Answer

The correct partial fraction decomposition of $\frac{5}{x^2 + 5x}$ is $\frac{1}{x} - \frac{1}{x + 5}$. This is because the denominator can be factored as $x(x + 5)$, and the decomposition must account for each linear factor in the denominator.

Write the Partial Fraction Decomposition of the Rational Expression 5x2+5x\frac { 5 } { x ^ { 2 } + 5 x }x2+5x5​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 5 } { x ^ { 2 } + 5 x }$