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

Question

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

Quizplus · Accepted Answer

The denominator $x^3 - x$ can be factored as $x(x^2 - 1) = x(x - 1)(x + 1)$. The partial fraction decomposition of the given expression should involve terms with denominators $x$, $x - 1$, and $x + 1$. Option B correctly decomposes the given expression into fractions with these denominators and coefficients that, when combined, yield the original numerator upon finding a common denominator and adding the fractions.

Write the Partial Fraction Decomposition of the Rational Expression 3x2−3x−2x3−x\frac { 3 x ^ { 2 } - 3 x - 2 } { x ^ { 3 } - x }x3−x3x2−3x−2​

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