Answer
$(2,\infty)$.
Work Step by Step
1. $\frac{x+1}{x-2}\ge1 \Longrightarrow \frac{x+1}{x-2}-1\ge0 \Longrightarrow \frac{3}{x-2}\ge0$
2. Identify boundary points $x=2$ and form intervals $(-\infty,2),(2,\infty)$.
3. Choose test values for each interval $x=0,3$ and test the inequality to get $False,\ True$.
4. Thus we have the solution $(2,\infty)$.
