Answer
$(-\infty,-4)U[1,\infty)$
Work Step by Step
Step 1. The domain requirements for this function is $\frac{x-1}{x+4}\ge0$
Step 2. The boundary points are $x=-4,1$ dividing the x-axis into $(-\infty,-4),(-4,1],[1,\infty)$
Step 3. Use test values $x=-5,0,2$ to test the inequality and we can get the result as $True,\ False,\ True$
Step 4. Thus the domain is $(-\infty,-4)U[1,\infty)$