Problem with splitting a long fractional equation

Question

I have a long equation

\begin{equation}
\Theta_{K} (\Delta t, \omega_{L}) = \frac{A}{2} \left[\frac{exp(-\Delta t/T_{2}^{*})\left[exp(- i \omega_{L} \Delta t)\left(exp(t_{rep}/T_{2}^{*} - i \omega_{L} t_{rep} - 1)\right) + exp(i \omega_{L} \Delta t) \left(exp(t_{rep}/T_{2}^{*} + i \omega_{L} t_{rep} - 1)\right) \right]}{exp\left(2 t_{rep}/T_{2}^{*}\right) + 1 - 2Re \left(exp(t_{rep}/T_{2}^{*} + i \omega_{L} t_{rep} - 1)\right)}\right]
\end{equation}

which does not fit on single line. How can I split this over two lines?

Answer 1

You can factor out common sub-expressions.

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator\RE{Re}
\newcommand\trep{t_{\mathrm{rep}}}
\begin{document}
\begin{align}
\hspace{-1em}
\Theta_{K} (\Delta t, \omega_{L})
    &= \frac{A}{2}
       \left[\frac{\exp(-\Delta t/T_{2}^{*})\left[\Phi(-1)+\Phi(+1)\right]}%
                  {\exp\left(2 \trep/T_{2}^{*}\right) + 1 - 2\RE \left(\exp(\trep/T_{2}^{*}
                   + i \omega_{L} \trep - 1)\right)}\right]\\
\intertext{where}
\Phi(\sigma) &= 
\exp(\sigma\omega_{L} \Delta t)\exp(\trep/T_{2}^{*} +\sigma i \omega_{L} \trep - 1)\notag
\end{align}
\end{document}