calculus - Limit of: $lim_{xrightarrowinfty}left(frac{x+2}{x+1}right)^{x/2}$

Without the use of L'hospitals rule, solve the following:

$$\lim_{x\rightarrow\infty}\left(\frac{x+2}{x+1}\right)^{x/2}$$

I'm trying to apply the limit that says

$$\lim_{x\rightarrow\pm\infty} \left(1+\frac{1}{x}\right)^x = e$$

However, I'm confused as the exponent is now $x/2$ and $x$ is approaching positive infinity in the limit, and not $\pm\infty$. Also there's the rational.

Thank you in advance