Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$$\frac { 5 x + 4 } { ( x + 7 ) ( x + 6 ) ^ { 2 } }$$
A) $\frac { A } { x + 7 } + \frac { B } { x + 6 } + \frac { C } { x + 6 } + \frac { D } { ( x + 6 ) ^ { 2 } }$
B) $\frac { A } { x + 7 } + \frac { B } { x + 6 } + \frac { C x + D } { ( x + 6 ) ^ { 2 } }$
C) $\frac { A } { x + 7 } + \frac { B } { x + 6 } + \frac { C } { ( x + 6 ) ^ { 2 } }$
D) $\frac { \mathrm { A } } { \mathrm { x } + 7 } + \frac { \mathrm { B } } { \mathrm { x } + 6 } + \frac { \mathrm { C } } { \mathrm { x } + 6 } + \frac { \mathrm { Dx } + \mathrm { E } } { ( \mathrm { x } + 6 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

For a repeated linear factor $(x + 6)^2$, the partial fraction decomposition includes terms for each power up to the highest power present, hence $\frac{A}{x+7} + \frac{B}{x+6} + \frac{C}{(x+6)^2}$ is the correct form.

Write the Form of the Partial Fraction Decomposition of the Rational