Find the partial fraction decomposition. (Hint: Use the rational zero theorem to factor the denominator.)
-$$\frac { 11 x ^ { 2 } + 19 x - 7 } { x ^ { 3 } + 2 x ^ { 2 } - 15 x - 36 }$$
A) $\frac { 6 } { x + 3 } + \frac { - 5 } { ( x + 3 ) ^ { 2 } } + \frac { 5 } { x - 4 }$
B) $\frac { - 5 } { x + 3 } + \frac { 6 } { ( x + 3 ) ^ { 2 } } + \frac { - 5 } { x - 4 }$
C) $\frac { - 5 x + 6 } { ( x + 3 ) ^ { 2 } } + \frac { - 5 } { x - 4 }$
D) $\frac { 6 x - 5 } { ( x + 3 ) ^ { 2 } } + \frac { 5 } { x - 4 }$

Question

Quizplus · Accepted Answer

First, factor the denominator: $x^3 + 2x^2 - 15x - 36 = (x + 3)^2(x - 4)$. Then, decompose the fraction accordingly, matching the given options.

Find the Partial Fraction Decomposition 11x2+19x−7x3+2x2−15x−36\frac { 11 x ^ { 2 } + 19 x - 7 } { x ^ { 3 } + 2 x ^ { 2 } - 15 x - 36 }x3+2x2−15x−3611x2+19x−7​

Find the Partial Fraction Decomposition $\frac { 11 x ^ { 2 } + 19 x - 7 } { x ^ { 3 } + 2 x ^ { 2 } - 15 x - 36 }$