Answer
$\displaystyle \frac{y+1}{y-1}$
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.
$\displaystyle \frac{y}{y-1}-\frac{1}{1-y}\cdot \displaystyle \frac{-1}{-1} =\displaystyle \frac{y}{y-1}-\frac{-1}{-(1-y)}$
$=\displaystyle \frac{y}{y-1}-\frac{-1}{y-1} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$
$=\displaystyle \frac{y}{y-1}+\frac{1}{y-1}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
= $\displaystyle \frac{y+1}{y-1}$
