Answer
The simplified form of the expression $\frac{3}{y-1}-\frac{y}{1-y}$ is $\frac{3+y}{y-1}$.
Work Step by Step
$\frac{3}{y-1}-\frac{y}{1-y}$
Obtain the alternative form of the expression by multiplying the rational expression $\frac{3}{y-1}-\frac{y}{1-y}$ by 1 in the form$\frac{-1}{-1}$:
$\begin{align}
& \frac{3}{y-1}-\frac{y}{1-y}=\frac{3}{y-1}-\frac{y}{1-y}.1 \\
& =\frac{3}{y-1}-\frac{y}{1-y}.\frac{-1}{-1}
\end{align}$
Apply the Distributive property:
$\begin{align}
& \frac{3}{y-1}-\frac{y}{1-y}=\frac{3}{y-1}-\frac{y}{1-y}.\frac{-1}{-1} \\
& =\frac{3}{y-1}-\frac{-\left( y \right)}{-\left( 1-y \right)} \\
& =\frac{3}{y-1}+\frac{y}{y-1}
\end{align}$
Now, the denominators are same. So, add the numerators and keep the common denominator:
$\begin{align}
& \frac{3}{y-1}-\frac{y}{1-y}=\frac{3}{y-1}+\frac{y}{y-1} \\
& =\frac{3+y}{y-1}
\end{align}$