Answer
$(−∞,1)$ U $(2,∞)$
Work Step by Step
$-1/(x-1) > -1$
$-1/(x-1)*(x-1) > -1*(x-1)$
$-1 > -1(x-1)$
$-1 > -x +1 $
$-1+1+x > -x+1+1+x$
$x > 2$
The denominator is zero when $x=1$.
We have three sections: $(−∞,1)$, $(1,2)$, and $(2,∞)$. We need to test one value for x in each section to determine if the section would be a solution set. Since we have the $>$ sign, we exclude the end points and use parentheses instead of brackets.
Let $x=0$, $x=1.5$, and $x=3$
$x=0$
$-1/(x-1) > -1$
$-1/(0-1) > -1$
$-1/-1 > -1$
$1 > -1$ (true)
$x=1.5$
$-1/(x-1) > -1$
$-1/(1.5-1) > -1$
$-1/.5>-1$
$-2 > -1$ (false)
$x=3$
$-1/(x-1) > -1$
$-1/(3-1) > -1$
$-1/2 > -1$ (true)
