% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage{ProfLycee}

\begin{document}

\begin{tikzpicture}[x=0.6cm,y=0.6cm,xmin=-4,xmax=15,xgrille=1,xgrilles=0.5,ymin=-5,ymax=8,ygrille=1,ygrilles=0.5]
	\GrilleTikz \AxesTikz[ElargirOx=0/0,ElargirOy=0/0]
	\AxexTikz[Police=\footnotesize]{-4,-3,...,14}
	\AxeyTikz[Police=\footnotesize]{-5,-4,...,7}
	\draw[red] (3.1,7.7) node[right,font=\large] {$\mathcal{C}_2$} ;
	\draw[blue] (3.1,-4) node[right,font=\large] {$\mathcal{C}_1$} ;
	\clip (\xmin,\ymin) rectangle (\xmax,\ymax) ;
	\draw[very thick,red,dashed,domain=3.1:15.5,samples=500] plot (\x,{(2*\x-1)/(\x*\x-\x-6)}) ;
	\draw[very thick,blue,domain=3.001:15.5,samples=500] plot (\x,{ln(\x*\x-\x-6)}) ;
\end{tikzpicture}

\end{document}