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 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

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

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