حاصل $\underset{x\to +\infty }{\mathop{\lim }}\,(\frac{{{x}^{۲}}}{x-۱}-\frac{{{x}^{۲}}-x}{x+۱})$ کدام است؟
$\underset{x\to +\infty }{\mathop{\lim }}\,(\frac{{{x}^{2}}}{x-1}-\frac{{{x}^{2}}-x}{x+1})=\underset{x\to +\infty }{\mathop{\lim }}\,\frac{{{x}^{2}}(x+1)-({{x}^{2}}-x)}{(x-1)(x+1)}=\underset{x\to +\infty }{\mathop{\lim }}\,\frac{{{x}^{3}}+{{x}^{2}}-{{x}^{3}}+{{x}^{2}}+{{x}^{2}}-x}{{{x}^{2}}-1}=\underset{x\to +\infty }{\mathop{\lim }}\,\frac{3{{x}^{2}}-x}{{{x}^{2}}-1}=3$