Suggestions for splitting a large fractional equation?

I might consider taking a slightly different approach, and use something like the following

This allows you to split f and g as you like

\documentclass{article}

\usepackage{mathtools}


\begin{document}

We have that
\[
p_{ij,k} = \begin{dcases}
\frac{f(\tau,\eta)}{g(\tau,\eta)}& \textrm{ if }j \in N_i\\
0&\textrm{ otherwise}\\
\end{dcases}
\]
where
\begin{align*}
f(\tau,\eta)&=[\tau_{ij,1}]^{\lambda_k \alpha} \cdot [\tau_{ij,2}]^{(1-\lambda_k)\alpha} 
            \cdot   [\eta_{ij,1}]^{\lambda_k \beta} \cdot [\eta_{ij,2}]^{(1-\lambda_k)\beta}\\
g(\tau,\eta)&=\sum_{h \in N_i} [\tau_{ih,1}]^{\lambda_k \alpha} \cdot [\tau_{ih,2}]^{(1-\lambda_k)\alpha} 
            \cdot [\eta_{ih,1}]^{\lambda_k \beta} \cdot [\eta_{ih,2}]^{(1-\lambda_k)\beta}
\end{align*}

\end{document}

Note that dcases is from the mathtools package. If the journal you're submitting doesn't have this, you could replace it with cases but the display won't be quite as good.

best I could come up with was:

\documentclass{amsart}

\begin{document}

\begin{equation}
p_{ij,k} = \begin{cases}
\dfrac{
\begin{split}
  [\tau_{ij,1}]^{\lambda_k \alpha} \cdot [\tau_{ij,2}]^{(1-\lambda_k)\alpha} \cdot \qquad\\  
[\eta_{ij,1}]^{\lambda_k \beta} \cdot [\eta_{ij,2}]^{(1-\lambda_k)\beta}
\end{split}
}{
\begin{split}
\sum_{h \in N_i} [\tau_{ih,1}]^{\lambda_k \alpha} \cdot [\tau_{ih,2}]^{(1-\lambda_k)\alpha} \cdot \qquad\\
[\eta_{ih,1}]^{\lambda_k \beta} \cdot [\eta_{ih,2}]^{(1-\lambda_k)\beta}
\end{split}
}& \textrm{ if }j \in N_i\\
0&\textrm{ otherwise}\\
\end{cases}
\end{equation}

\end{document}

use \sum\limits_{h \in N_i} for the sum. It needs less space. And use \text instead of \textrm