Find the partial fraction decomposition for the rational expression.
-$$\frac { 4 x ^ { 2 } + 3 x + 56 } { \left( x ^ { 2 } - 64 \right) ( x - 1 ) }$$
A) $\frac { 2 } { x - 8 } + \frac { 3 } { x + 8 } + \frac { 1 } { x - 1 }$
B) $\frac { 5 } { x ^ { 2 } - 64 } + \frac { - 1 } { x - 1 }$
C) $\frac { 5 } { x - 8 } + \frac { 3 } { x + 8 } + \frac { - 2 } { x - 1 }$
D) $\frac { 3 } { x - 8 } + \frac { 2 } { x + 8 } + \frac { - 1 } { x - 1 }$

Question

Quizplus · Accepted Answer

The denominator $x^2 - 64$ can be factored into $(x - 8)(x + 8)$, making the decomposition involve terms with denominators $x - 8$, $x + 8$, and $x - 1$. The coefficients are determined by algebraic manipulation to ensure the original expression is equivalent to the sum of the partial fractions.

Find the Partial Fraction Decomposition for the Rational Expression 4x2+3x+56(x2−64)(x−1)\frac { 4 x ^ { 2 } + 3 x + 56 } { \left( x ^ { 2 } - 64 \right) ( x - 1 ) }(x2−64)(x−1)4x2+3x+56​

Find the Partial Fraction Decomposition for the Rational Expression $\frac { 4 x ^ { 2 } + 3 x + 56 } { \left( x ^ { 2 } - 64 \right) ( x - 1 ) }$