Restricting tikz plot to multiple domains due to dividing by zero

I'm trying to plot a formula where for my intended domain, a division by zero will be done. Overleaf/latex gives me the following error: Dimension Too Large. I think this has to do with each other. That is why I try restrict the plotting around the asymptotes. The mathematical problem is that there are poles at +3.5 and -3.5 ; here is a link to wolframalpha, showcasing the function: link

Inspired by link, I tried to implement it the following way, without success.

Do you have suggestions how I can restrict an tikz plot for multiple domains. I could split the function into multiple \addplot. However, I do not prefer this, as in my real report I'm plotting a lot off functions

\begin{figure}[ht]
\begin{tikzpicture}
\begin{axis}[
xmin=-9, xmax=9,
ymin=0, ymax=5,
% domain = -9:9
]

%   restrict expr to domain={(x>=-9)&&(x<=-3.4)||(x>=-3.6)&&(x<=3.4)||(x>=3.6)&&(x<=9)}{1:1},
samples=100,
line width=0.45mm,
color=blue,
]
{(3)/(x+3.5)^2 + (3)/(3.5-x)^2 + 3 * e^(-((0-x)^2)/ (2 * 1^2))};

\end{axis}
\end{tikzpicture}
\end{figure}

• Welcome to TeX.SE! Please always provide MWE (Minimal Working Example), a small but complete document, which reproduce your problem. Jul 4 at 14:24
• Ah, I tried to do that. But you mean with \begin{document} etc? Jul 4 at 15:46
• Yes, as I do in my answer. Many times are information in document preamble essential for the solving of problem, However in this not forget on "minimal" ;-) Jul 4 at 15:59

Like this?

By use of restrict y to domain =<min>:<max> ,:

\documentclass[border=3.141592]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis lines=center,
xlabel = {$x$}, xlabel style = {anchor=west},
ylabel = {$y$},
xmin=-9, xmax=9, xtick={-8,-6,...,8},
extra  x ticks = {0},
ymin=0,  ymax=27,
tick label style = {font=\scriptsize},
domain = -8.5:8.5,
restrict y to domain = 0:100,
no marks,
every axis plot post/.append style={very thick},
]