Addition and Subtraction

\begin{equation*}
\begin{split}
&\frac{x}{1}+\frac{2x-3}{3}+\frac{4-x}{4}\\\\
&\frac{12x}{12}+\frac{4(2x-3)}{12}+\frac{3(4-x)}{12}\:\:\:\:\:\color {blue} \text{the least common denominator is 12}\\\\
&\frac{12x+4(2x-3)+3(4-x)}{12}\\\\
&\frac{12x +8x - \cancel{12} + \cancel{12} - 3x}{12}\\\\
&\frac{17x}{12}
\end{split}
\end{equation*}