Calculate $\lim_{x\to\infty}\frac{x^2}{x+1}-\sqrt{x^2+1}$

Hint: $\displaystyle\lim_{x\to\infty}\frac{x^2}{x+1}-\sqrt{x^2+1}=\lim_{x\to\infty}\left(\frac{x^2}{x+1}-x\right)+\lim_{x\to\infty}\left(x-\sqrt{x^2+1}\right)$