Answer
$\text{LCM}= x-5$.
Work Step by Step
Given \begin{equation}
\frac{2 x}{5-x},\quad \frac{3 x}{x-5}.
\end{equation} Note the the first fraction can be rewritten as: \begin{equation}
\begin{aligned}
\frac{2 x}{5-x}&=\frac{2 x}{-(x-5)} \\
&=\frac{-2 x}{x-5}.\\
\end{aligned}
\end{equation} The two fractions now have the same denominator. Hence, the $\textbf{LCM}= x-5$.
