\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}

\begin{displaymath}
{{\rho_i}\over{\rho_j}} = 
{
{T_{j \rightarrow i} \times  A_{j \rightarrow i}}
\over
{T_{i \rightarrow j} \times  A_{i \rightarrow j} }
}
=
{
{\exp\{-\beta [U({\bf r}_i) - U({\bf r}_j)]\}}
\over
{1}
}
=
{
{\exp[-\beta U({\bf r}_i)]}
\over
{\exp[-\beta U({\bf r}_j)]}
}
\end{displaymath}

\end{document}