Answer
$(-\infty,3)U(8,\infty)$.
Work Step by Step
Step 1. For $\frac{x+2}{x-3}-2\lt0 \Longrightarrow \frac{-x+8}{x-3}\lt0$, identify the boundary points $x=3,8$.
Step 2. Form intervals $(-\infty,3),(3,8),(8,\infty)$.
Step 3. Choose test values for each interval $x=0,4,9$.
Step 4. Test the inequality and get results $True,\ False,\ True.$
Step 5. Thus we have the solution $(-\infty,3)U(8,\infty)$.
