Let f(x)=6x+12x24x12\displaystyle {f{{\left({x}\right)}}}={\frac{{{6}{x}+{12}}}{{{x}^{{2}}-{4}{x}-{12}}}}.

Calculate limx2f(x)\displaystyle \lim_{{{x}\to-{2}}}{f{{\left({x}\right)}}} by first finding a continuous function which is equal to f\displaystyle {f} everywhere except x=2\displaystyle {x}=-{2}.

limx2f(x)=\displaystyle \lim_{{{x}\to-{2}}}{f{{\left({x}\right)}}}=