Calculus problem with negative infinity $$\lim_{x\to-\infty} x(\sqrt{x²+1}-x)$$

Can someone simplify this and explain the steps. I'm having problems getting rid of sqrt.
No need to get rid of the square root.  As $x\to -\infty$, both $\sqrt{x^2+1}$ and $-x$ go to $+\infty$, and thus the product goes to $-\infty$.
At infinity sqrt( x^2+1) tends to x. So we have for the limitation process something like Lim x (x - x) as x tends to zero. I think it is an undefined condition and says nothing ...