Answer
(-infinity, $5)$ U $(6$, infinity)
Work Step by Step
$(x-5)/(x-6) > 0$
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)