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