Answer
(-infinity, $-1)$ U $(4$, infinity)
Work Step by Step
$(x+1)/(x-4) \geq0$
Denominator is zero when $x=4$
Numerator is zero when $x=-1$
(-infinity, $-1)$
$(-1, 4)$
$(4$, infinity)
Let $x=-10$, $x=0$, $x=10$
$x=-10$
$(x+1)/(x-4) \geq0$
$(-10+1)/(-10-4) \geq0$
$-11/-14 \geq 0$
$11/14 \geq 0$ (true)
$x=0$
$(x+1)/(x-4) \geq0$
$(0+1)/(0-4) \geq0$
$1/-4 \geq 0$
$-1/4 \geq 0$ (false)
$x=10$
$(x+1)/(x-4) \geq0$
$(10+1)/(10-4) \geq0$
$11/6 \geq 0$(true)
