Find the partial fraction decomposition for the rational expression.
-$\frac { 560 x ^ { 2 } + 320 x } { \left( x ^ { 2 } + 4 \right) ( x + 6 ) }$
A) $\frac { 104 x + 456 } { x ^ { 2 } + 4 } + \frac { - 304 } { x + 6 }$
B) $\frac { 104 x } { x + 6 } + \frac { 152 } { x ^ { 2 } + 4 }$
C) $\frac { 104 x - 304 } { x ^ { 2 } + 4 } + \frac { - 456 } { x + 6 }$
D) $\frac { 104 x - 304 } { x ^ { 2 } + 4 } + \frac { 456 } { x + 6 }$

Question

Quizplus · Accepted Answer

The partial fraction decomposition involves expressing the rational expression as a sum of fractions with simpler denominators. Solving for coefficients, we find that the correct decomposition is $\frac { 104 x - 304 } { x ^ { 2 } + 4 } + \frac { 456 } { x + 6 }$.

Find the Partial Fraction Decomposition for the Rational Expression 560x2+320x(x2+4)(x+6)\frac { 560 x ^ { 2 } + 320 x } { \left( x ^ { 2 } + 4 \right) ( x + 6 ) }(x2+4)(x+6)560x2+320x​

Find the Partial Fraction Decomposition for the Rational Expression $\frac { 560 x ^ { 2 } + 320 x } { \left( x ^ { 2 } + 4 \right) ( x + 6 ) }$