حاصل $\underset{x\to \pm \infty }{\mathop{\lim }}\,\frac{{{(x+۲)}^{۳}}-{{(x-۲)}^{۳}}}{{{(x+۲)}^{۲}}+{{(x-۲)}^{۲}}}$ کدام است؟
$\begin{align} & \underset{x\to \pm \infty }{\mathop{\lim }}\,\frac{{{(x+2)}^{3}}-{{(x-2)}^{3}}}{{{(x+2)}^{2}}+{{(x-2)}^{2}}} \\ & =\underset{x\to \pm \infty }{\mathop{\lim }}\,\frac{({{x}^{3}}+6{{x}^{2}}+12x+8)-({{x}^{3}}-6{{x}^{2}}+12x-8)}{({{x}^{2}}+4x+4)({{x}^{2}}-4x+4)} \\ & =\underset{x\to \pm \infty }{\mathop{\lim }}\,\frac{12{{x}^{2}}+16}{2{{x}^{2}}+8}=\frac{12}{2}=6 \\ \end{align}$