Answer
$=\displaystyle \frac{11}{x-1}$
Work Step by Step
When one denominator is the opposite, or additive inverse of the other,
first multiply either rational expression by $\displaystyle \frac{-1}{-1}$
to obtain a common denominator.
$\displaystyle \frac{6}{x-1}-\frac{5}{1-x} \cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{6}{x-1}-\frac{-5}{-(1-x)}$
$= \displaystyle \frac{6}{x-1}-\frac{-5}{x-1} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$
$= \displaystyle \frac{6}{x-1}+\frac{5}{x-1}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
$=\displaystyle \frac{6+5}{x-1}$
$=\displaystyle \frac{11}{x-1}$
