I believe to solve expressions like: 

$$\lim\_{x\to \infty} (2x^2 + 1)$$

we need to divide each term in the numerator and denominator by the highest power. In the previous case, the highest power is $x^2$, so we get

$$\lim\_{x \to \infty} \left(2 + \frac{1}{x^2} \right) = 2+0=2$$

Now for: 

$$\lim\_{n \to \infty} \frac{-1}{\sqrt{n} + 2}$$

The answer given is $\frac{-1}{\infty}=0$ 

On the other hand, what I did was 

$$\lim\_{x \to \infty} \frac{-1}{1 + \frac{2}{\sqrt{n}}}=\frac{-1}{1}=-1$$

What's wrong?