Write the partial fraction decomposition of the rational expression.
-$$\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$$
A) $\frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$
B) $\frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } - \frac { 2 } { x + 11 }$
C) $- \frac { 8 } { x + 8 } - \frac { 2 } { x + 2 } - \frac { 2 } { x + 11 }$
D) $- \frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$

Question

Quizplus · Accepted Answer

The partial fraction decomposition of the given rational expression involves breaking it down into simpler fractions. The correct decomposition is $\frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$, which matches option A. This can be verified by finding constants A, B, and C such that $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) } = \frac { A } { x + 8 } + \frac { B } { x + 2 } + \frac { C } { x + 11 }$, and solving for A, B, and C.

Write the Partial Fraction Decomposition of the Rational Expression 12x2+162x+384(x+8)(x+2)(x+11)\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }(x+8)(x+2)(x+11)12x2+162x+384​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$