Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 798: 16

(-infinity, $5)$ U $(6$, infinity)

$(x-5)/(x-6) > 0$ Denominator is zero when $x=6$ $x-5=0$ $x=5$ (-infinity, $5)$ $(5, 6)$ $(6$, infinity) Let $x=0$, $x=5.5$, $x=10$ $x=0$ $(x-5)/(x-6) > 0$ $(0-5)/(0-6) > 0$ $-5/-6 > 0$ $5/6 > 0$ (true) $x=5.5$ $(x-5)/(x-6) > 0$ $(5.5-5)/(5.5-6) > 0$ $.5/-.5 > 0$ $-1 > 0$ (false) $x=10$ $(x-5)/(x-6) > 0$ $(10-5)/(10-6) > 0$ $5/4 > 0$ (true)