\documentclass{article}
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\begin{document}
\DIFdelbegin \DIFdel{An }\DIFdelend \DIFaddbegin \DIFadd{No }\DIFaddend equation with different subscripts
\DIFdelbegin \[\DIFdel{
a_r=a_\beta+a_{i+j}
}\]
%DIFAUXCMD
\DIFdel{and the same with superscripts
}\[\DIFdel{
a^r=a^\beta+a^{i+j}
}\]
%DIFAUXCMD
\DIFdelend \DIFaddbegin 

\DIFadd{and none with superscripts
}

\DIFaddend Now an equation that is in both \DIFaddbegin \DIFadd{but subtly different
}\DIFaddend \[
E=mc\DIFdelbegin \DIFdel{^3}\DIFdelend \DIFaddbegin \DIFadd{^2}\DIFaddend \ \ \ \ x=1+\sin y\DIFdelbegin \DIFdel{^{i+j+\cdots}
}\DIFdelend \DIFaddbegin \DIFadd{^{i+j+k+\cdots}
}\DIFaddend \]
\DIFdelbegin \DIFdel{and equation using }%DIFDELCMD < \verb|\left| %%%
\DIFdel{and }%DIFDELCMD < \verb|\right|
%DIFDELCMD < 

%DIFDELCMD < %%%
\[\DIFdel{
S=\left    \{ 5+\smile+\frac{numerator}{denominator} \right \}
}\]
%DIFAUXCMD
\DIFdelend 


\end{document}
