\begin{tikzpicture}[scale=0.7]

\pgfplotsset{compat=1.11}

\definecolor{FireBrick}{rgb}{0.7, 0.13, 0.13}

\definecolor{NewBlue}{rgb}{0.27, 0.45, 0.76}

\tikzfading[name=arrowfading, top color=transparent!0, bottom color=transparent!95]
\tikzset{arrowfill/.style={#1,general shadow={fill=black, shadow yshift=-0.8ex, path fading=arrowfading}}}
\tikzset{arrowstyle/.style n args={3}{draw=#2,arrowfill={#3}, single arrow,minimum height=#1, single arrow,
		single arrow head extend=.3cm,}}

%\NewDocumentCommand{\tikzfancyarrow}{O{2cm} O{FireBrick} O{top color=orange!20!red, bottom color=red} m}{
%\tikz[baseline=-0.5ex]\node [arrowstyle={#1}{#2}{#3}] {#4};
%}


%\node [
%  fill=blue!50, draw, 
%  single arrow,  single arrow head indent=0ex,
%  rotate=0, 
%  font=\sffamily
%] at (1,1.5) 
%{\rotatebox{0}{ \qquad}};


%\draw[color=gray!10,step=2mm,help lines] (-0.7,0) grid (72mm,58mm);
%\draw[color=gray!70,step=10mm,xshift=4mm,yshift=-1mm] (-0.5,0) grid (70mm,60mm);
\begin{axis}[
x=1cm,y=1cm,
axis x line=center,
axis y line=center,
%axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-5,
xmax=5,
ymin=-6,
ymax=5,
xtick={-4,-3,...,4},
ytick={-5,-4,...,4},]
\addplot [mark=none,domain=-4.8:-1.05, color=NewBlue, line width=0.5mm,step=10000, smooth, tension=0.2] {1/(x^2-1)};
\addplot [mark=none,domain=-0.95:0.95, color=NewBlue, line width=0.5mm,step=10000] {1/(x^2-1)};
\addplot [mark=none,domain=1.05:4.8, color=NewBlue, line width=0.5mm,step=10000] {1/(x^2-1)};

%\clip(-17.083986586441775,-20.54798056618339) rectangle (4.103328404466779,7.349328615703948);
\end{axis}
\draw[-latex,red, line width=0.75mm](6.15,2.5) node[above, right, yshift=0.5mm] {von rechts} -- (4.15,2.5) ;
%\node[] (A) at ( 1,3) {\textbf{$y^2=x^2$}};

\end{tikzpicture}