Find the partial fraction decomposition of 1x3−x\frac{1}{x^3 - x}x3−x1.
1x+1x−1+1x+1\frac{1}{x} + \frac{1}{x-1} + \frac{1}{x+1}x1+x−11+x+11
−1x+12(x−1)+12(x+1)-\frac{1}{x} + \frac{1}{2(x-1)} + \frac{1}{2(x+1)}−x1+2(x−1)1+2(x+1)1
1x−12(x−1)−12(x+1)\frac{1}{x} - \frac{1}{2(x-1)} - \frac{1}{2(x+1)}x1−2(x−1)1−2(x+1)1
−1x+1x−1−1x+1-\frac{1}{x} + \frac{1}{x-1} - \frac{1}{x+1}−x1+x−11−x+11