# Suggestions for splitting a large fractional equation?

I have seen a number of questions detailing specific means for how to break down a given equation, however I am more interested in the design at this point. That is, I'm not sure what part of this equation is suitable to be split. I have an equation that will not fit in a single column as is:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
$$p_{ij,k} = \begin{cases} \frac{ [\tau_{ij,1}]^{\lambda_k \alpha} \cdot [\tau_{ij,2}]^{(1-\lambda_k)\alpha} \cdot [\eta_{ij,1}]^{\lambda_k \beta} \cdot [\eta_{ij,2}]^{(1-\lambda_k)\beta} } { \sum_{h \in N_i} [\tau_{ih,1}]^{\lambda_k \alpha} \cdot [\tau_{ih,2}]^{(1-\lambda_k)\alpha} \cdot [\eta_{ih,1}]^{\lambda_k \beta} \cdot [\eta_{ih,2}]^{(1-\lambda_k)\beta} } & \textrm{ if }j \in N_i \\ 0&\textrm{ otherwise} \\ \end{cases}$$
\end{document}​


The problem is that both the numerator and the denominator would need to be split, and I'm not sure of a way to do this that would still look appropriate. Any suggestions?

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.

• I thought it might come to that. Very elegant. Thanks. – Andrew Jan 31 '12 at 20:15

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

• This seems more like a comment than an answer. Would you agree? – Werner Jan 31 '12 at 20:15
• no, I don't agree – user2478 Jan 31 '12 at 20:24

best I could come up with was:

\documentclass{amsart}

\begin{document}

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

\end{document}

• Greatly appreciate the effort, but I don't think a journal will accept it. – Andrew Jan 31 '12 at 20:09
• Ah If it's a journal their copy editors will reformat it anyway so just send it as it is:-) Otherwise as suggested in the other answer introducing some local definitions to restructure the expression is probably the way to go. – David Carlisle Jan 31 '12 at 20:13