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