Write the partial fraction decomposition of the rational expression.
-$\frac { 6 x ^ { 2 } - x - 11 } { x ^ { 3 } - x }$
A) $\frac { 11 } { x } + \frac { - 2 } { x + 1 } + \frac { - 3 } { x - 1 }$
B) $\frac { 11 } { x } + \frac { 2 } { x + 1 } + \frac { - 3 } { x - 1 }$
C) $\frac { 11 } { x } + \frac { - 2 } { x + 1 } + \frac { 3 } { x - 1 }$
D) $\frac { 11 } { x } + \frac { - 3 } { x + 1 } + \frac { 2 } { x - 1 }$

Question

Quizplus · Accepted Answer

The denominator $x^3 - x$ can be factored as $x(x^2 - 1) = x(x - 1)(x + 1)$. The partial fraction decomposition of the given expression will have the form $\frac{A}{x} + \frac{B}{x + 1} + \frac{C}{x - 1}$. Solving for A, B, and C using the method of partial fractions, we find that $A = 11$, $B = -2$, and $C = -3$, which matches option A.

Write the Partial Fraction Decomposition of the Rational Expression 6x2−x−11x3−x\frac { 6 x ^ { 2 } - x - 11 } { x ^ { 3 } - x }x3−x6x2−x−11​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 6 x ^ { 2 } - x - 11 } { x ^ { 3 } - x }$