Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$$\frac { 7 x - 5 } { x ^ { 2 } + 9 x + 18 }$$
A) $\frac { A } { x + 6 } + \frac { B } { x + 3 } + \frac { C x + D } { x ^ { 2 } + 9 x + 18 }$
B) $\frac { A } { x + 6 } + \frac { B } { x + 3 } + \frac { C } { x ^ { 2 } + 9 x + 18 }$
C) $\frac { A } { x + 6 } + \frac { B } { x + 3 }$
D) $\frac { A } { x + 6 } + \frac { B } { x + 3 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 3 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The denominator $x^2 + 9x + 18$ can be factored into $(x + 6)(x + 3)$, and since these are distinct linear factors, the partial fraction decomposition will consist of terms of the form $\frac{A}{x + 6} + \frac{B}{x + 3}$ without any quadratic terms or repeated factors.

Write the Form of the Partial Fraction Decomposition of the Rational