lean_workbook_plus_16454

Alternatively, you can notice that the sum or product of an odd number of negatives is a negative. All squares must be non-negative. So we know $(x-1)^2$ is always positive (or zero, but that would make it false), so we only have to worry about $\frac{(x-2)}{(x-3)}$ . $x-2$ is positive if $x>2$ and negative if $x<2$ , and $x-3$ is positive if $x>3$ and negative if $x<3$ . We want one of them will be positive and the other will be negative to get a negative quotient. This happens if $2<x<3$ , or $\boxed{(2,3)}$ .