Answer
$ (-1,\frac{2}{3})U(2,\infty)$
Work Step by Step
Step 1. Factor the denominator $x^3+1=(x+1)(x^2-x+1)$. Identify boundary points (zeros and asymptotes) as $x=-1,\frac{2}{3},2$ which divide the x-axis into four intervals $(-\infty,-1),(-1,\frac{2}{3}),(\frac{2}{3},2),(2,\infty)$
Step 2. Choose test values in each interval $x=-2,0,1,3$ and test the inequality to get $False,\ True,\ False,\ True$
Step 3. Thus the solution intervals are $ (-1,\frac{2}{3})U(2,\infty)$
