## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

The simplified form of the expression $\frac{3}{y-1}-\frac{y}{1-y}$ is $\frac{3+y}{y-1}$.
$\frac{3}{y-1}-\frac{y}{1-y}$ 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}