\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}
\xi^0 & = & \frac{\xi_O}{m} = \frac{\xi_C}{n} \\
\frac{\beta_O}{\sqrt{m}} & = & \frac{\beta_C}{\sqrt{n}} = \xi^0 \frac{\sqrt{m}+\sqrt{n}}{2}\\
\end{eqnarray*}

\end{document}