Breaking the equation inside a fraction

Question

I am trying to write this equation using the help provided in the link below

How to break a long expression in the denominator of a fraction?

Still the equation goes outside the margin. I using \documentclass[a4paper,10pt]{article}.

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
%opening
\title{}
\author{}

\begin{document}    
\maketitle

\begin{abstract}   
\end{abstract}

\section{}    

\begin{equation*}
-\dfrac{1}{128\pi^{2}}\left[\dfrac{\splitdfrac{4(m_1 + m_3)\cos~\delta~\sin\theta_{12}~\sin\theta_{13}(\cos~\delta~\cos~\theta_{12}(2~y_e^{2} 
- y_\mu^{2} - y_\tau^{2} +(y_\mu^{2} - y_\tau^{2})\cos~2\theta_{23})\sin~\theta_{13}}{+ (-y_\mu^{2} + y_\tau^{2})\sin~
\theta_{12}~\sin~2\theta_{23}}}{m_1 - m_3}\right] + 
\end{equation*}    
\end{document}

Answer 1

\documentclass[a4paper]{article}
\usepackage{mathtools}

\begin{document}
\begin{equation}
\dfrac{1}{128\pi^{2}}
\left[\dfrac{\splitdfrac{
4(m_1 + m_3)\cos \delta \sin\theta_{12} \sin\theta_{13}(
\cos \delta \cos \theta_{12}(2 y_e^{2} - y_\mu^{2} - y_\tau^{2}}{ +(y_\mu^{2} -y_\tau^{2})\cos 2\theta_{23})\sin \theta_{13} + 
(-y_\mu^{2} + y_\tau^{2})\sin 
\theta_{12} \sin 2\theta_{23})}}
{m_1 - m_3}\right]
\end{equation}

\end{document}

Answer 2

Here, I suggest an alternative to avoid the ugly split numerator.

\documentclass[a4paper]{article}
\usepackage[usestackEOL]{stackengine}
\stackMath
\begin{document}
\begin{equation}
\frac{1}{128\pi^{2}}
\left[\frac{Q}
{m_1 - m_3}\right]
\end{equation}

where

\[
\setstackgap{S}{4pt}
\Shortstack[r]{Q = 
4(m_1 + m_3)\cos \delta \sin\theta_{12} \sin\theta_{13}(
\cos \delta \cos \theta_{12}(2 y_e^{2} - y_\mu^{2} - y_\tau^{2}\\ +(y_\mu^{2} -y_\tau^{2})\cos 2\theta_{23})\sin \theta_{13} + 
(-y_\mu^{2} + y_\tau^{2})\sin 
\theta_{12} \sin 2\theta_{23})}
\]

\end{document}

Answer 3

The problem is that the only item getting placed in the lower half of the \splitdfrac was the + symbol, and everything else was being placed on a single line. It’s easier to see in a screenshot of the fraction (this was taken in landscape):

Look at how the + appears to be typeset below everything else, and then the rest of the numerator continues on a different baseline.

Here's a cleaned up version of the code, that is hopefully a little easier to read/follow and compiles to a slightly less wide/more compact fraction:

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\begin{equation}
  -\frac{1}{128 \pi^2}
  \left[
    \frac{
      \splitfrac{
        4 (m_1+m_3) \cos\delta \sin\theta_{12} \sin\theta_{13}
        (\cos\delta \cos\theta_{12} (2\,y_e^2 - y_\mu^2 - y_\tau^2
      }{
        + (y_\mu^2 - y_\tau^2) \cos 2\theta_{23})) \sin\theta_{13}
        + (-y_\mu^2 + y_\tau^2) \sin\theta_{12} \sin 2\theta_{23}
      }
    }{
      m_1 - m_3
    }
  \right]
\end{equation}

\end{document}

Here's a screenshot of the new equation:

And some other comments:

• As David Carlisle says in the comments, you should be using \sin or \cos for math operators; not just typing out the words in italic maths font. Additionally, don’t use non-breaking spaces (the tildes ~) in maths mode. Instead, consider using maths-spaces (such as the thin space \, that I’ve used above).

• Consider breaking your fraction up into multiple lines, to make it easier to read and debug. That was the first thing I did, and then the out-of-place + leapt out at me. The scheme above perhaps isn't perfect, but I claim it’s better than a single monolithic line.

• You don't need curly braces around exponents with a single character (e.g. y^2 rather than y^{2}). Again, might make things easier to read (but that's a personal preference).

Answer 4

To make it easier on your readers to parse the many terms in the numerator, you may want to break the entire expression across three lines. Note also that I have -- like the other responders too -- replaced all Sin and Cos occurrences with \sin and \cos and have deleted all ~ spacer elements.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
-\frac{1}{128\pi^{2}}\,
\dfrac{\left(
\splitdfrac{\splitdfrac{4(m_1 + m_3) \cos\delta\sin\theta_{12}\sin\theta_{13}}{{}\times[\cos\delta\cos\theta_{12}
(2y_e^{2} - y_\mu^{2} - y_\tau^{2} +
(y_\mu^{2} -y_\tau^{2})\cos2\theta_{23}]
\sin\theta_{13}}}{+(-y_\mu^{2} + y_\tau^{2})
\sin \theta_{12}\sin2\theta_{23}}\right)}{m_1 - m_3}
\end{equation}
\end{document}