Answer
$ (-3,0)\cup(0,3) $.
Work Step by Step
Step 1. For $x^4-9x^2\lt0 \Longrightarrow x^2(x+3)(x-3)\lt0$, identify boundary points as $x=-3,0,3$.
Step 2. Form intervals $(-\infty,-3),(-3,0),(0,3),(3,\infty)$.
Step 3. Choose test values for each interval $x=-4,-1,1,4$.
Step 4. Test the inequality to get results: $False,\ True,\ True,\ False$
Step 5. We have the solution $ (-3,0)\cup(0,3) $.
