\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
xmin=-5, xmax=5,
ymin=-5, ymax=5,
xlabel=$x$, ylabel=$y$,
domain=-10:10, samples=200,
restrict y to domain=-10:10,
enlargelimits={abs=1cm},
axis line style={latex-latex},
ticklabel style={font=\tiny,fill=white},
xtick={-2,1}, ytick={1},
yticklabels={1},
xticklabels={-2,1},
xlabel style={below right},
ylabel style={above left},
xlabel={$x$},
ylabel={$y$},
axis line style={->},
]
\addplot[red, thick, domain=-10:-2] {(x-1)/(x+2)};
\addplot[red, thick, domain=-2:10] {(x-1)/(x+2)};
\draw[dashed] ({rel axis cs:0,0} -| {axis cs:-2,0}) -- ({rel axis cs:0,1} -| {axis cs:-2,0});
\draw[dashed] ({rel axis cs:1,0} |- {axis cs:0,1}) -- ({rel axis cs:0,1} -| {axis cs:1,0});
\end{axis}
\end{tikzpicture}