Find the partial fraction decomposition for the rational expression.
-$$\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }$$
A) $\frac { 4 } { 3 x + 4 } + \frac { 2 } { ( x + 1 ) ^ { 2 } } + \frac { - 3 } { x + 1 }$
B) $\frac { 4 } { 3 x + 4 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } } + \frac { - 2 } { x + 1 }$
C) $\frac { 4 } { 3 x + 4 } + \frac { 3 } { ( x + 1 ) ^ { 2 } } + \frac { 2 } { x + 1 }$
D) $\frac { 4 } { 3 x + 4 } + \frac { - 2 } { x + 1 } + \frac { 3 } { ( x + 1 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition involves expressing the rational expression as a sum of fractions with denominators that are powers of the factors of the original denominator. The correct coefficients are found by equating and solving for the numerators.

Find the Partial Fraction Decomposition for the Rational Expression −2x2+3x+8(x+1)2(3x+4)\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }(x+1)2(3x+4)−2x2+3x+8​

Find the Partial Fraction Decomposition for the Rational Expression $\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }$