Answer
$(-\infty,3)U(8,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{x+2}{x-3}-2\lt0 \longrightarrow \frac{-x+8}{x-3}\lt0$
Step 2. Identify the boundary points as $x=3,8$ and the intervals $(-\infty,3),(3,8),(8,\infty)$
Step 3. Choose test values $x=0,4,9$ in each interval and test the inequality to get $True,\ False,\ True$
Step 4. Thus we get the solution interval(s) $(-\infty,3)U(8,\infty)$
