\documentclass[tikz,border=3mm]{book}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[thick, scale=2,cyan]
\begin{axis}[
xmin=-5, xmax=5,
ymin=-1, ymax=1,
samples=700,
axis y line=center,
axis x line=middle
]
\addplot+[mark=none,smooth,color=magenta] {(x)/(1+x^2)};
\end{axis}
\end{tikzpicture}
\[y=\frac{x}{1+x^2}\]
\end{center}
\end{document}