Making a new environment combining equation and split

The reason that \begin{split} ... \end{split} doesn't work when the \begin ... \end are invoked within the begin and end parts of another environment is related to the reason given in the "technical notes on the amsmath package" (texdoc technote) -- the parsing requires an exact match of the environment specified by \begin{...}.

this isn't really obvious from the current documentation in technote, but it would be a good idea to add it, and I'll try to arrange for that to happen.

I wouldn't have expected this, but there's an easy answer; thanks to Stefan Kottwitz! (And thanks to Will Robertson for writing the package environ that I had never heard of before. He should have given this answer; with his package it works like a charm.)

\documentclass{article}
\usepackage{amsmath,environ}
\NewEnviron{example}{%
\begin{equation}\begin{split}
  \BODY
\end{split}\end{equation}
}
\begin{document}
\begin{example}
a &= b + c \\
  &= d + e
\end{example}
\end{document}

Some explanations can be found in Stefan's post behind the above link.

The split environment has to be used within a math displaying environment. I guess that what you are trying to do is to create a shortcut so that you don't have to write

\begin{equation}
\begin{split}
...
\end{split}
\end{equation}

every time.

Perhaps an alternative to split would be the aligned environment which also allows you align a sequence of formulas on the equal sign and, placing it inside an equation environment, you also get a single equation number for the whole expression. Also luckily, aligned doesn't have the parsing problems of split and plays well with new environment definitions.

\usepackage{amsmath}
\newenvironment{equations}{\equation\aligned}{\endaligned\endequation}

\begin{equations}
a &= b + c \\
  &= d + e
\end{equations}

Of course, you can always read the documentation from amsmath by typing

texdoc amsldoc

on a command line to find inspiration and browse for alternatives.