$\lim_{n \to \infty} \frac{\lg(1 + n)}{n} = \lim_{n \to \infty} \frac{1}{1 + n}$

Question

I have found this in part of a proof from https://walkccc.github.io/CLRS/Chap03/3.2/, question 3.2-5:

$\lim_{n \to \infty} \frac{\lg(1 + n)}{n} = \lim_{n \to \infty} \frac{1}{1 + n}$

I'm not able see how to go from one to the next. I understand the idea that lg(1+n) is smaller than n.