Write the partial fraction decomposition of the rational expression. $\frac { 7 x ^ { 2 } - 3 x - 6 } { x ^ { 3 } - x }$
A) $\frac { 6 } { x } + \frac { 2 } { x - 1 } - \frac { 1 } { x - 1 }$
B) $\frac { 6 } { x } + \frac { 2 } { x + 1 } + \frac { 1 } { x - 1 }$
C) $\frac { 6 } { x } - \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$
D) $\frac { 6 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x + 1 }$
E) $\frac { 6 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$

Question

Write the partial fraction decomposition of the rational expression.​ $\frac { 7 x ^ { 2 } - 3 x - 6 } { x ^ { 3 } - x }$ ​
A) $\frac { 6 } { x } + \frac { 2 } { x - 1 } - \frac { 1 } { x - 1 }$
B) $\frac { 6 } { x } + \frac { 2 } { x + 1 } + \frac { 1 } { x - 1 }$
C) $\frac { 6 } { x } - \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$
D) $\frac { 6 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x + 1 }$
E) $\frac { 6 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$

Quizplus · Accepted Answer

The denominator $x^3 - x$ can be factored as $x(x^2 - 1) = x(x - 1)(x + 1)$. The correct partial fraction decomposition must account for each of these factors, and option E correctly decomposes the given fraction into partial fractions with denominators $x$, $x + 1$, and $x - 1$, with appropriate numerators.

Write the Partial Fraction Decomposition of the Rational Expression 7x2−3x−6x3−x\frac { 7 x ^ { 2 } - 3 x - 6 } { x ^ { 3 } - x }x3−x7x2−3x−6​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 7 x ^ { 2 } - 3 x - 6 } { x ^ { 3 } - x }$