Answer
The simplified form of the rational expression $\frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}$ is $-\frac{3x}{2}$.
Work Step by Step
$\frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}$
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,
$\begin{align}
& \frac{x-y}{2x}\cdot \frac{3{{x}^{2}}}{y-x}=\frac{x-y}{x-y}\cdot \frac{-3x\cdot x}{2\cdot x} \\
& =1\cdot \frac{x}{x}\cdot \frac{-3x}{2} \\
& =1\cdot \frac{-3x}{2} \\
& =-\frac{3x}{2}
\end{align}$
