# How do you combine 1/(x-1) - x/(x-1)?

The two fractions have the same denominator, $x - 1$, so you can add directly the numerators getting:
$\frac{1}{x - 1} - \frac{x}{x - 1} = \frac{1 - x}{x - 1} = - \frac{x - 1}{x - 1} = - 1$