Answer
$(2,7/2)$
Work Step by Step
$3/ (x-2) > 2$
$x-2=0$
$x-2+2=0+2$
$x=2$
The denominator is zero when $x=2$
$3/(x-2) = 2$
$3*(x-2)/(x-2) =2*(x-2)$
$3 = 2*(x-2)$
$3/2 =2*(x-2)/2$
$3/2 = x-2$
$3/2 + 2 = x-2+2$
$7/2 =x$
Three regions to test: $(-∞, 2)$, $(2,7/2)$, $(7/2, ∞)$
Let $x=0$, $x=3$, $x=4$
$x=0$
$3/ (x-2) > 2$
$3/ (0-2) > 2$
$3/-2 > 2$
$-3/2 > 2$ (false)
$x=3$
$3/ (x-2) > 2$
$3/ (3-2) > 2$
$3/1 > 2$
$3 > 2$ (true)
$x=4$
$3/ (x-2) > 2$
$3/ (4-2) > 2$
$3/2 > 2$ (false)
