Answer
$[-2, 3]$
Work Step by Step
$(x-3)/(x+2) \le 0$
The denominator is zero when $x=-2$, and the numerator is zero when $x=3$.
We have three sections: $(−∞,-2)$, $(-2, 3)$, and $(3,∞)$. We need to test one value for x in each section to determine if the section would be a solution set. Since we have the $\le$ sign, we include the end points and use brackets instead of parentheses.
Let $x=-3$, $x=0$, and $x=4$
$x=-3$
$(x-3)/(x+2) \le 0$
$(-3-3)/(-3+2) \le 0$
$-6/-1 \le 0$
$6 \le 0$ (false)
$x=0$
$(x-3)/(x+2) \le 0$
$(0-3)/(0+2) \le 0$
$-3/2 \le 0$ (true)
$x=4$
$(x-3)/(x+2) \le 0$
$(4-3)/(4+2) \le 0$
$1/6 \le 0$ (false)
