Answer
$(5,6)$
Work Step by Step
$(x-5)/ (x-6) < 0$
The denominator is zero when $x=6$.
$(x-5)/ (x-6) < 0$
$(x-5)/ (x-6) = 0$
$(x-5)/ (x-6)*(x-6) = 0*(x-6)$
$x-5=0$
$x-5+5=0+5$
$x=5$
Three regions to test: $(-∞, 5)$, $(5,6)$, $(6,∞)$
Let $x=0$, $x=5.5$, $x=7$
$x=0$
$(x-5)/ (x-6) < 0$
$(0-5)/ (0-6) < 0$
$-5/ -6 < 0$
$5/6 < 0$ (false)
$x=5.5$
$(x-5)/ (x-6) < 0$
$(5.5-5)/ (5.5-6) < 0$
$.5/-.5 <0$
$-1 < 0$ (true)
$x=7$
$(x-5)/ (x-6) < 0$
$(7-5)/ (7-6) < 0$
$2/1 < 0$
$2 < 0$ (false)
