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

Question

Quizplus · Accepted Answer

The given expression $\frac { 1 } { x ^ { 2 } + 2 x }$ can be factored as $\frac { 1 } { x(x + 2) }$. The correct partial fraction decomposition separates each factor in the denominator, leading to $\frac { A } { x } + \frac { B } { x + 2 }$.

Write the Form of the Partial Fraction Decomposition of the Rational