No continuous hyperbola in tikz

I am trying to draw an hyperbola with the simple function f(x) = x/(x-1) in tikz inside the axis environment. However, when the programme draws the function it pictures a straightline where the function is not define, namely x=1.

I have tryied to mended it by adding a second plot and restricting the domains, and even though it works latex would come with the following error: ‘Dimension too large’

Is there a proper way to remove it? Below the code and the result (for my amendment just uncommend the line above the addplot and restrict domanins).

KR

documentclass[usenames,dvipsnames]{beamer}

%usetheme{CambridgeUS}

definecolor{Red}{RGB}{176,23,31}


%% Useful packages
usepackage{lipsum,graphicx,subcaption}
usepackage{float}
usepackage{amsmath}
usepackage{amssymb}
usepackage{mathtools}
usepackage{bm}
usepackage{mathrsfs}
usepackage{amsfonts}


usepackage{tikz}
    usetikzlibrary{decorations.pathreplacing}
    usetikzlibrary{fit, calc, matrix, positioning, arrows.meta, intersections, through, backgrounds, patterns}
usepackage{pgfplots}
    pgfplotsset{compat = newest}
    usepgfplotslibrary{fillbetween}
    pgfplotsset{overwrite option/.style args={#1 with #2}{#1=#2,#1/.code=}}
    pgfplotsset{
        vasymptote/.style={before end axis/.append code={draw[dashed,<->,-{Latex}] ({rel axis cs:0,0} -| {axis cs:#1,0}) -- ({rel axis cs:0,1} -| {axis cs:#1,0}); }},
        myaxis/.style={axis line style={<->, {Latex}-{Latex}}}
        }   % This fancy shit sets the arrows to both parts of the axis in

begin{document}
begin{frame}{FUNCTIONS}
    framesubtitle{BASICS}
    textbf{Domain}: the set of numbers (inputs) for which the function has defined outputs.
    
    textbf{Example:}
    vspace{-20pt
    }
    begin{columns}
        column{.4textwidth}
        begin{figure}
            centering
            begin{tikzpicture}
    begin{axis}[
        width=6cm,
        xscale = 1, yscale = 1,
        axis lines = middle,
        myaxis,
        grid,
        grid style={densely dashed},
        xmin = -5.5, xmax = 5.5, ymin = -5.5, ymax = 5.5,
        every axis/.append style={font=tiny},
        xlabel = {$x$}, xlabel style={at=(current axis.right of origin), anchor=west},
        ylabel = $y$, ylabel style={at=(current axis.above origin), anchor=east},
        xtick = {-4,-2,0,2,4},
        % xticklables = {-2,0,2,4,6},
        ytick = {-4,-2,0,2,4},
        % yticklables = {-2,0,2,4,6},
        samples=100,
        domain=-5.5:5.5,
        axis equal,
        % no markers
        ]
        addplot[domain=-5:5, thick, RoyalBlue, name path = rb]{ln(x)} node[above, rotate = 0] at (2,2) {$f(x) = ln(x)$} ;
    end{axis}
end{tikzpicture}
            caption*{$Domleft(f(x)right) = left{ forall xin mathbb{R} | x>0right}$}
            % label{fig:my_label}
        end{figure}
        
        column{.4textwidth}
        begin{figure}
            centering
            begin{tikzpicture}
    begin{axis}[
        width=6cm,
        xscale = 1, yscale = 1,
        axis lines = middle,
        myaxis,
        grid,
        grid style={densely dashed},
        xmin = -5.5, xmax = 5.5, ymin = -5.5, ymax = 5.5,
        every axis/.append style={font=tiny},
        xlabel = {$x$}, xlabel style={at=(current axis.right of origin), anchor=west},
        ylabel = $y$, ylabel style={at=(current axis.above origin), anchor=east},
        xtick = {-4,-2,0,2,4},
        % xticklables = {-2,0,2,4,6},
        ytick = {-4,-2,0,2,4},
        % yticklables = {-2,0,2,4,6},
        samples=100,
        domain=-5.5:5.5,
        axis equal,
        % no markers
        ]
        % addplot[domain=-5:1, thick, YellowOrange, name path = rb]{x/(x-1)} ;
        addplot[domain=-6:6, thick, YellowOrange, name path = rb]{x/(x-1)} node[above, rotate = 0] at (3,3) {$g(x) = frac{x}{x-1}$} ;
    end{axis}
end{tikzpicture}
            caption*{$Domleft(g(x)right) = left{ forall xin mathbb{R} | xin mathbb{R}backslash x=1 right}$}
            % label{fig:my_label}
        end{figure}
        
    end{columns}
    
end{frame}
end{document}

documentclass[usenames,dvipsnames]{beamer}
%usetheme{CambridgeUS}
    setbeamerfont{caption}{size=footnotesize}
definecolor{Red}{RGB}{176,23,31}
%% Useful packages
usepackage{lipsum,graphicx,subcaption}
%usepackage{float}% have not sense in beamer presentations
usepackage{mathrsfs}
usepackage{mathtools, amssymb} % mathtools load amsmath, amssymb load amsfonts
usepackage{bm}

usepackage{pgfplots} % it loads tikz too
pgfplotsset{compat = 1.17}
usepgfplotslibrary{fillbetween}
usetikzlibrary{arrows.meta,
                backgrounds,
                calc,
                decorations.pathreplacing,
                fit,
                intersections,
                matrix,
                patterns, positioning,
                through}

begin{document}
begin{frame}{FUNCTIONS}
    framesubtitle{BASICS}
    textbf{Domain}: the set of numbers (inputs) for which the function has defined outputs.

    textbf{Example:}
%vspace{-20pt}

pgfplotsset{
    width=6cm,
    axis lines = middle,
    grid,
    grid style={densely dashed},
    xmin = -5.5, xmax = 5.5, ymin = -5.5, ymax = 5.5,
    every axis/.append style={font=tiny},
    xlabel = {$x$}, xlabel style={anchor=west},
    ylabel = $y$,   ylabel style={anchor=east},
    xtick = {-4,-2,0,2,4},
    ytick = {-4,-2,0,2,4},
    samples=100,
    axis equal,
            }
 
    begin{columns}
        column{.45textwidth}
        begin{figure}
            begin{tikzpicture}
    begin{axis}
        addplot[domain=-5:5, thick, RoyalBlue] {ln(x)} node[above left] {$f(x) = ln(x)$} ;
    end{axis}
end{tikzpicture}
    caption*{$mathrm{Dom}left(f(x)right) = left{ forall xin mathbb{R}mid x>0right}$}
        end{figure}
%
        column{.52textwidth}
        begin{figure}
            begin{tikzpicture}
    begin{axis}
addplot[domain=-5:0.9, thick, YellowOrange]{x/(x-1)} ;
addplot[domain= 1.01:6, thick, YellowOrange]{x/(x-1)} node[xshift=1em,above left] {$g(x) = frac{x}{x-1}$} ;
    end{axis}
end{tikzpicture}
    caption*{$mathrm{Dom}left(g(x)right) = left{forall xin mathbb{R}mid xin mathbb{R}neg{x}=1 right}$}
        end{figure}
    end{columns}

end{frame}
end{document}