Some examples.
For any positive real numbers $a,b,c$ we have $$\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3.$$ This inequality follows from the following inequality: \begin{equation} x+y+z\ge 3\sqrt[3]{xyz} \forall x,y,z\ge 0. \label{eq:amgm} \end{equation}
The inequality \eqref{eq:amgm} is the well-known AM-GM inequality.
Results:
For any positive real numbers $a,b,c$ we have $$\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3.$$ This inequality follows from the following inequality: \begin{equation} x+y+z\ge 3\sqrt[3]{xyz}\quad \forall x,y,z\ge 0. \label{eq:amgm} \end{equation}
The inequality \eqref{eq:amgm} is the well-known AM-GM inequality.