Answer
$(5, 6)$
Work Step by Step
$(x-5)/(x-6) < 0$
$x=5$ makes the numerator 0, while $x=6$ makes the denominator 0. Three regions to test: $(-infinity, 5)$, $(5, 6)$, $(6, infinity)$
Let $x=0$, $x=5.5$, $x=10$
$x=0$
$(x-5)/(x-6) < 0$
$(0-5)/(0-6) < 0$
$-5/-6 < 0$
$5/6 < 0$ (false)
$x=5.5$
$(x-5)/(x-6) < 0$
$(5.5-5)/(5.5-6) < 0$
$.5/-.5 < 0$
$-1 < 0$ (true)
$x=10$
$(x-5)/(x-6) < 0$
$(10-5)/(10-6) < 0$
$5/4 < 0$ (false)
