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

The simplified form of the rational expression $\frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}$ is $-\frac{3x}{2}$.
$\frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}$ Obtain the alternative form of the expression by multiplying the rational expression $\frac{3{{x}^{2}}}{y-x}$ by 1 in the form $\frac{-1}{-1}$. So, \begin{align} & \frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}=\frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}\cdot \frac{-1}{-1} \\ & =\frac{x-y}{2x}\cdot \frac{-3{{x}^{2}}}{x-y} \end{align} Regroup and remove the factor equal to 1, \begin{align} & \frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}=\frac{x-y}{x-y}\cdot \frac{-3x\cdot x}{2\cdot x} \\ & =1\cdot \frac{x}{x}\cdot \frac{-3x}{2} \\ & =1\cdot \frac{-3x}{2} \\ & =-\frac{3x}{2} \end{align}