Find the partial fraction decomposition.
-$\frac { - 31 x - 46 } { 2 x ^ { 2 } + 10 x + 8 }$
A) $- \frac { 5 } { 2 x - 2 } - \frac { 13 } { x - 4 }$
B) $- \frac { 5 } { x + 2 } - \frac { 13 } { 2 x + 4 }$
C) $\frac { 5 } { 2 x + 2 } + \frac { 13 } { x + 4 }$
D) $- \frac { 5 } { 2 x + 2 } - \frac { 13 } { x + 4 }$

Question

Quizplus · Accepted Answer

First, factor the denominator: $2x^2 + 10x + 8 = 2(x^2 + 5x + 4) = 2(x + 1)(x + 4)$. The partial fraction decomposition is of the form $\frac{A}{x + 1} + \frac{B}{x + 4}$. Multiplying both sides by the common denominator yields $-31x - 46 = A(x + 4) + B(x + 1)$. Solving for A and B gives $A = -5$ and $B = -13$, leading to the decomposition $- \frac{5}{2(x + 1)} - \frac{13}{x + 4}$, which simplifies to choice D.

Find the Partial Fraction Decomposition −31x−462x2+10x+8\frac { - 31 x - 46 } { 2 x ^ { 2 } + 10 x + 8 }2x2+10x+8−31x−46​

Find the Partial Fraction Decomposition $\frac { - 31 x - 46 } { 2 x ^ { 2 } + 10 x + 8 }$