Answer
$ (2,\infty)$.
Work Step by Step
Step 1. Rewrite the inequality as $\frac{x+1}{x-2}-1\ge0$ or $\frac{3}{x-2}\ge0$.
Step 2. Identify the boundary point(s) $x=2$ and intervals $(-\infty,2),(2,\infty)$.
Step 3. Choose test values for each interval $x=0,3$ and test the inequality to get $False,\ True$.
Step 4. We can identify the solution intervals $ (2,\infty)$.
