\documentclass[border=4pt]{standalone}
\usepackage{xcolor}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage{xparse}
\usepackage{calc}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{calc}
\usepackage{tikz}

\newcommand{\longdivision}[2]{
    \settowidth{\DividendOneLength}{#1}
    \settowidth{\DividendTwoLength}{#2}
    \settoheight{\DividendOneHeight}{#1}
    \settoheight{\DividendTwoHeight}{#2}
    \settoheight{\MaxHeight}{#1#2}

    \begin{tikzpicture} [baseline=.5pt]
        \node at (.23*\DividendTwoLength+5pt ,   .5*\DividendTwoHeight) {#2};
        \node at (.35*\DividendOneLength+5pt , 2.2*\DividendOneHeight) {#1};
        \draw [Thin]  (-10pt,-.22*\DividendOneHeight) arc (-70:60:\MaxHeight*.41 and \MaxHeight*1.82) -- ++(\DividendOneLength+5pt,0pt);
    \end{tikzpicture}
}

\newlength{\DividendOneLength}
\newlength{\DividendTwoLength}
\newlength{\DividendOneHeight}
\newlength{\DividendTwoHeight}
\newlength{\MaxHeight}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\PhantC}{\phantom{\colon}}%
\newcommand{\PhantSQ}{\phantom{\sqrt{\hspace{.3ex}}}}%

\ExplSyntaxOn
\makeatletter
\newcommand{\CMidRule}{\noalign\bgroup\@CMidRule{}}
\NewDocumentCommand{\@CMidRule}{
    m
    O{0.0ex}
    O{0.0ex}
    m
}{
    \peek_meaning_remove_ignore_spaces:NTF \CMidRule
      { \@CMidRule { #1 \cmidrule[\cmidrulewidth](l{#2}r{#3}){#4} } }
      { \egroup #1 \cmidrule[\cmidrulewidth](l{#2}r{#3}){#4} }
}
\makeatother
\ExplSyntaxOff

\begin{document}

\[
\begin{array}{rll}
       a_1\colon      & \multicolumn{1}{l}{x+y}                                                                                                            \\
       a_2\colon      & \multicolumn{1}{l}{1}                                                                                     &\qquad\,\,\,r       \\
   xy + 1\PhantC   & \multirow{1}*{\longdivision{$x^2y+x y^2+y^2$}{$x^2y-x$}}                                                     \\  \cline{3-3}
y^2 + 1\PhantC   &\\

                           &\PhantSQ                                                                                                                                    \\  \CMidRule[3.0ex]   [9.0ex]{2-2}
                           &\PhantSQ \hphantom{x^2y +{}}  xy^2 +      x +      y^2                                                               \\
                           &\PhantSQ \hphantom{x^2y +{}}  xy^2 -                                  y                                                   \\  \CMidRule[9.0ex]  [5.0ex]{2-2}
                           &\PhantSQ \hphantom{x^2y +       xy^2 +{}} x +      y^2 +       y                                                   \\  \CMidRule[16.0ex][5.0ex]{2-2}
                           &\PhantSQ \hphantom{x^2y +       xy^2 +      x +{}} y^2 +       y                        & \to x                 \\
                           &\PhantSQ \hphantom{x^2y +       xy^2 +      x +{}} y^2 -                    1                                       \\  \CMidRule[20.0ex][5.0ex]{2-2}
                           &\PhantSQ \hphantom{x^2y +       xy^2 +      x +      y^2 +{}}  y +       1                                       \\  \CMidRule[25.0ex][1.0ex]{2-2}
                           &\PhantSQ \hphantom{x^2y +       xy^2 +      x +      y^2 +       y +{}}  1            &\to x+y              \\  \CMidRule[25.0ex][1.0ex]{2-2}
                           &\PhantSQ \hphantom{x^2y +       xy^2 +      x +      y^2 +       y +{}}  0            &\to x+y+1
\end{array}
\]


\end{document}