# Breaking equation - Problem with brackets

I want to break a long equation in LaTex. I have tried multline and align but I always get errors with the brackets.

$$\dfrac{dr_{ij}}{dt} = \frac{1}{2r_{ij}} \left[ 2 \left( x_{i}-x_{j} \right) \left( \dfrac{dx_{i}}{dt} - \dfrac{dx_{j}}{dt} \right) + 2 \left( y_{i}-y_{j} \right) \left( \dfrac{dy_{i}}{dt} - \dfrac{dy_{j}}{dt} \right) + 2 \left( z_{i}-z_{j} \right) \left( \dfrac{dz_{i}}{dt} - \dfrac{dz_{j}}{dt} \right) \right]$$


I want to break it in a way, so that all the three "2"s are below each other. How can I do that without getting an error with the brackets?

This is a job for split:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$$\begin{split} \frac{dr_{ij}}{dt} = \frac{1}{2r_{ij}} \biggl[ & 2 \left( x_{i}-x_{j} \right) \left( \dfrac{dx_{i}}{dt} - \dfrac{dx_{j}}{dt} \right) + {}\\ & 2 \left( y_{i}-y_{j} \right) \left( \dfrac{dy_{i}}{dt} - \dfrac{dy_{j}}{dt} \right) + {}\\ & 2 \left( z_{i}-z_{j} \right) \left( \dfrac{dz_{i}}{dt} - \dfrac{dz_{j}}{dt} \right) \biggr] \end{split}$$
\end{document}


Note that we have to manually specify the size for the outermost braces, because \left and \right cannot be divided across lines.

• you should probably also mention that you've specified the size of the outermost brackets manually instead of using \left ... \right, since those can't be separated across lines. Apr 21, 2014 at 15:35
• Is there any way to use \left ... \right or any way that adapts the brackets' size automatically? Apr 21, 2014 at 19:41
• @user50224 Sorry, no. Apr 21, 2014 at 19:50
• @egreg: Ok, but in your answer: Why are the brackets before "dx" and especially after "dxj" not aligned perfectly below each other? Apr 21, 2014 at 19:54
• @user50224 I try to avoid compound fractions in the first place. \left[<formula>\right. and \left.<formula>\right] with some \vphantom may help. Apr 21, 2014 at 20:13

If you need to split large brackets across lines of an equation, it's easiest to set their size manually.

\documentclass[10pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\dfrac{dr_{ij}}{dt} = \frac{1}{2r_{ij}} \biggl[
&2 ( x_{i}-x_{j}) \left( \dfrac{dx_{i}}{dt} - \dfrac{dx_{j}}{dt} \right) \nonumber \\
{}+{} &2 ( y_{i}-y_{j}) \left( \dfrac{dy_{i}}{dt} - \dfrac{dy_{j}}{dt} \right) \nonumber \\
{}+{} &2 ( z_{i}-z_{j}) \left( \dfrac{dz_{i}}{dt} - \dfrac{dz_{j}}{dt} \right) \biggr]
\end{align}
\end{document}