%% 
%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
%%  3. Auflage
%%  Beispiel 10-04-9 auf Seite 220.
%%  Copyright (C) 2018 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%%  See http://www.latex-project.org/lppl.txt for details.
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\documentclass[10pt]{screxa}
\pagestyle{empty}
\setlength\textwidth{352.81416pt}
\AtBeginDocument{\setlength\parindent{0pt}}
%StartShownPreambleCommands
\usepackage{mathtools}
\newcommand*\num[1]{\hphantom{#1}} \newcommand*\vsp{\vphantom{\rangle_1}}
%StopShownPreambleCommands
\begin{document}
\begin{equation*}
  \frac{300}{5069} \underbrace{\longmapsto\vphantom{\frac{1}{1}}}_{%
    \mathclap{\substack{\Delta a=271\num9\vsp \\[2pt]
                        \Delta b=4579\vsp\\[2pt]
                        \text{$1$ iteration}}}}\frac{29}{490}
  \underbrace{\longmapsto \frac{19}{321}\longmapsto}_{%
    \mathclap{\substack{\Delta a=10\num{9}=\langle271\rangle_{29}\num{20}\\[2pt]
                        \Delta b=169=\langle4579\rangle_{490}\\[2pt]
                        \text{$2$ iterations}}}}\frac{9}{152}
  \underbrace{\longmapsto \frac{8}{135}\longmapsto\dots\longmapsto}_{%
    \substack{\Delta a=1\num{7}=\langle10\rangle_{9}\num{119}\\[2pt]
              \Delta b=17=\langle169\rangle_{152}\\[2pt]
             \text{$8$ iterations}}}\frac{1}{16}
  \underbrace{\longmapsto\dots\longmapsto\vphantom{\frac{8}{135}}}_{%
    \substack{\Delta a=0=\langle1\rangle_{1}\num{76} \\[2pt]
              \Delta b=1=\langle17\rangle_{16} \\[2pt]
              \text{$8$ iterations}}}\frac{1}{1}
\end{equation*}
\end{document}