Answer
$(−∞,-10)$ U $(10,∞)$
Work Step by Step
$(x+10)/(x-10) > 0$
The denominator is zero when $x=10$, and the numerator is zero when $x=-10$.
We have three sections: $(−∞,-10)$, $(-10, 10)$, and $(10,∞)$. 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 $>$ sign, we exclude the end points and use parentheses instead of brackets.
Let $x=-11$, $x=1$, and $x=11$
$x=-11$
$(x+10)/(x-10) > 0$
$(-11+10)/(-11-10) > 0$
$-1/-21 >0$
$1/21 >0$ (true)
$x=1$
$(x+10)/(x-10) > 0$
$(1+10)/(1-10) > 0$
$11/-9 >0$
$-11/9 > 0$ (false)
$x=11$
$(x+10)/(x-10) > 0$
$(11+10)/(11-10) > 0$
$21/1 > 0$
$21 >0$ (true)
