Calculate $\lim_{x\to\infty}\frac{x^2}{x+1}-\sqrt{x^2+1}$ I am stuck on a limit of the indeterminate form $\infty-\infty$. I have tried many approaches, such as multiplying with conjugates etc. and I am unable to find a solution. I suspect that there is an elementary trick that I am plainly missing right here. Can anybody give me a hint or solution as to solve
$$\lim_{x\to\infty}\frac{x^2}{x+1}-\sqrt{x^2+1}$$

$$\frac{x^2}{x-1}-\sqrt{1+x^2}=x+1+\frac1{x-1}-\sqrt{1+x^2}=1+\frac1{x-1}-\frac1{x+\sqrt{1+x^2}}$$hence $1$.
