Answer
$[1,2]\cup(3,\infty)$.
See graph.
Work Step by Step
Step 1. $\frac{(x-2)(x-1)}{x-3}\ge0 $, identify boundary points $x=1,2,3$.
Step 2. Form intervals $(-\infty,1],[1,2],[2,3),(3,\infty)$.
Step 3. Choose test values for each interval $x=0,1.5,2.5,4$.
Step 4. Test the inequality to get results $False,\ True,\ False,\ True$.
Step 5. Thus we have the solution $[1,2]\cup(3,\infty)$.
Step 6. See graph.
