# How to plot (sqrt(1+x)-sqrt(1-x))/x?

I am not able to get the correct graph of (sqrt(1+x)-sqrt(1-x))/x by using the following

\begin{tikzpicture}[scale=1,>=stealth]
\tkzInit[xmin=-1.5,xmax=1.5,ymin=0,ymax=2,xstep=0.5,ystep=0.5]
\tkzAxeXY[color=black!80]
\draw[scale=1,domain=-1:1,smooth,thick,variable=\x,red,->] plot ({\x},{((sqrt(1+\x)) - (sqrt(1-\x)))/(\x)});
\end{tikzpicture}


You only need to avoid the apparent singularity at 0, which can be achieved by setting the samples to an even number (for the symmetric domain at hand).

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tkz-euclide}
\begin{document}
\begin{tikzpicture}[scale=1,>=stealth]
\tkzInit[xmin=-1.5,xmax=1.5,ymin=0,ymax=2,xstep=0.5,ystep=0.5]
\tkzAxeXY[color=black!80]
\draw[scale=1,domain=-1:1,smooth,thick,variable=\x,red,->,samples=100]
plot ({\x},{((sqrt(1+\x)) - (sqrt(1-\x)))/(\x)});
\end{tikzpicture}
\end{document}


The result can be improved (IMHO) by bending the arrow and using pgfplots.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{arrows.meta,bending}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xmin=-1.5,xmax=1.5,ymin=0,ymax=2,axis lines=middle]