Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 799: 32

(-infinity, $-10)$

$(x+10)/(x-10) > 0$ Denominator is zero when $x=10$ $(x+10)/(x-10) = 0$ $(x+10)*(x-10)/(x-10) = 0*(x-10)$ $x+10 = 0$ $x=-10$ (-infinity, $-10)$ $(-10$, infinity) Let $x=-20$, $x=0$ $x=-20$ $(x+10)/(x-10) > 0$ $(-20+10)/(-20-10) > 0$ $-10/-30 > 0$ $1/3 > 0$ (true) $x=0$ $(x+10)/(x-10) > 0$ $(0+10)/(0-10) > 0$ $10/-10 >0$ $-1 >0$ (false)