Simplify $\frac {2\sqrt{x^2+x+1}-2-x} {x^2} $ In order to find the limit of the function at $0$ I need to simplify the fraction $$\frac {2\sqrt{x^2+x+1}-(2+x)} {x^2} $$
so that at $0$ it didn't look like $\frac 0 0$. I'm almost certain that it can be solved with a clever substitution of the variable but I didn't manage to find one.
I've also tried multiplying numerator and denominator by $2\sqrt{x^2+x+1}+2+x$, but without any success.

Multiplying numerator and denominator by $$2\sqrt{x^2+x+1}+2+x$$ we get
after simplification $$\frac{3x^2}{x^2(2\sqrt{x^2+x+1}+2+x)}$$ and after cancelling $$x^2$$ you will get the searched limit.
