[tex]\cfrac{\frac{a}{b}}{\frac{c}{ d}}\implies \cfrac{a}{b}\cdot \cfrac{ d}{c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{~~\frac{3x^2-3}{x^2+3x}~~}{\frac{x+1}{x(x+3)}}\implies \cfrac{3x^2-3}{x^2+3x}\cdot \cfrac{x(x+3)}{x+1}\implies \stackrel{\textit{common factoring}}{\cfrac{3(x^2-1)}{~~\begin{matrix}x (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} x (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{x+1}[/tex]
[tex]\textit{keeping in mind that}\qquad x^2-1\implies x^2-1^2\implies (x-1)(x+1) \\\\\\ \cfrac{\stackrel{~~\textit{difference of squares}}{3(x^2-1^2)~\hfill }}{x+1}\implies \cfrac{3(x-1)~~\begin{matrix} (x+1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\begin{matrix} (x+1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies 3(x-1)[/tex]
