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

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) $- \frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$

Quizplus · Accepted Answer

The partial fraction decomposition of the given rational expression is obtained by expressing it as a sum of fractions, where each fraction has a denominator that is a factor of the original denominator and a numerator that is a constant. By solving the equation $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) } = \frac { A } { x + 8 } + \frac { B } { x + 2 } + \frac { C } { x + 11 }$ for A, B, and C, we find that A = 8, B = 2, and C = 2, leading to the correct decomposition.

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 $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$