Write the partial fraction decomposition of the rational expression.
-$$\frac { - 28 x + 4 } { ( x - 3 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }$$
A) $\frac { - 6 x - 2 } { ( x - 3 ) ^ { 2 } } + \frac { - 2 x + 2 } { x ^ { 2 } + 1 }$
B) $\frac { 2 } { x - 3 } + \frac { - 8 } { ( x - 3 ) ^ { 2 } } + \frac { - 2 x + 2 } { x ^ { 2 } + 1 }$
C) $\frac { 2 } { x - 3 } + \frac { - 6 } { ( x - 3 ) ^ { 2 } } + \frac { - 2 x - 2 } { x ^ { 2 } + 1 }$
D) $\frac { 2 } { x - 3 } + \frac { - 8 } { ( x - 3 ) ^ { 2 } } + \frac { - 2 } { x ^ { 2 } + 1 }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition of the given rational expression involves breaking it down into simpler fractions that can be combined to form the original expression. The denominator $(x-3)^2(x^2+1)$ suggests that we need terms for $(x-3)$, $(x-3)^2$, and $(x^2+1)$. Option B correctly identifies these components, providing a term for each factor in the denominator.

Write the Partial Fraction Decomposition of the Rational Expression −28x+4(x−3)2(x2+1)\frac { - 28 x + 4 } { ( x - 3 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }(x−3)2(x2+1)−28x+4​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { - 28 x + 4 } { ( x - 3 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }$