limx→3(x3+x2−12xx2−9)=limx→3(x3−3x2+4x2−12x(x−3)(x+3))\lim\limits_{x \to 3} \left( \frac{x^{3}+x^{2}-12x}{x^{2}-9} \right) = \lim\limits_{x \to 3} \left( \frac{x^{3}-3x^{2}+4x^{2}-12x}{(x-3)(x+3)} \right)x→3lim(x2−9x3+x2−12x)=x→3lim((x−3)(x+3)x3−3x2+4x2−12x)
limx→3((x2+4x)(x−3)(x−3)(x+3)=limx→3(x2+4xx+3))\lim\limits_{x \to 3} \left( \frac{(x^{2}+4x)(x-3)}{(x-3)(x+3)} = \lim\limits_{x \to 3} \left( \frac{x^{2}+4x}{x+3} \right) \right)x→3lim((x−3)(x+3)(x2+4x)(x−3)=x→3lim(x+3x2+4x))
=32+4(3)3+3=216=72\frac{3^{2}+4(3)}{3+3} = \frac{21}{6} = \frac{7}{2}3+332+4(3)=621=27
