Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 799: 39

(-infinity, $2)$ U $(2$, infinity)

$-1/(x-1) > -1$ Denominator is zero when $x=1$ $-1/(x-1) > -1$ $-1/(x-1) = -1$ $-1*(x-1)/(x-1) = -1*(x-1)$ $-1=-x+1$ $-1+x+1=-x+1+x+1$ $x=2$ (-infinity, $2)$ $(2$, infinity) Let $x=0$ and $x=3$ $x=0$ $-1/(x-1) > -1$ $-1/(0-1) > -1$ $-1/-1 > -1$ $1 > -1$ (true) $x=3$ $-1/(x-1) > -1$ $-1/(3-1) > -1$ $-1/2 > -1$ (true)