Find the partial fraction decomposition of $\frac { 1 } { x ^ { 3 } - 4 x }$
A) $- \frac { 1 } { 4 x } + \frac { 1 } { 8 ( x - 2 ) } + \frac { 1 } { 8 ( x + 2 ) }$
B) $\frac { 1 } { x } + \frac { 1 } { 4 ( x - 2 ) } + \frac { 1 } { 2 ( x + 2 ) }$
C) $- \frac { 1 } { x } + \frac { 2 } { ( x - 2 ) } - \frac { 1 } { ( x + 2 ) }$
D) $\frac { 4 } { x } + \frac { 8 } { ( x - 2 ) } - \frac { 8 } { ( x + 2 ) }$

E)none

Question

Find the partial fraction decomposition of $\frac { 1 } { x ^ { 3 } - 4 x }$
A) $- \frac { 1 } { 4 x } + \frac { 1 } { 8 ( x - 2 ) } + \frac { 1 } { 8 ( x + 2 ) }$
B) $\frac { 1 } { x } + \frac { 1 } { 4 ( x - 2 ) } + \frac { 1 } { 2 ( x + 2 ) }$
C) $- \frac { 1 } { x } + \frac { 2 } { ( x - 2 ) } - \frac { 1 } { ( x + 2 ) }$
D) $\frac { 4 } { x } + \frac { 8 } { ( x - 2 ) } - \frac { 8 } { ( x + 2 ) }$

E)none

Quizplus · Accepted Answer

First, factor the denominator: $x^3 - 4x = x(x^2 - 4) = x(x - 2)(x + 2)$. The partial fraction decomposition is then of the form $\frac{A}{x} + \frac{B}{x - 2} + \frac{C}{x + 2}$. Solving for A, B, and C gives $A = -\frac{1}{4}$, $B = \frac{1}{8}$, and $C = \frac{1}{8}$, which matches option A.

Find the Partial Fraction Decomposition Of 1x3−4x\frac { 1 } { x ^ { 3 } - 4 x }x3−4x1​

Find the Partial Fraction Decomposition Of $\frac { 1 } { x ^ { 3 } - 4 x }$