For example
\[\frac{1}{2}=\frac{1}{3}+ \frac{1}{6}\]
The proof is quire simple.
Take unit fraction
\[\frac{1}{n}\]
.\[\begin{equation} \begin{aligned} \frac{1}{n+1} + \frac{1}{n(n+1)} &= \frac{n}{n(n+1)} + \frac{1}{n(n+1)} \\ &= \frac{n+1}{n(n+1)} \\ &= \frac{1}{n}\end{aligned} \end{equation}\]