calculus - How do I calculate/prove limits for exponential functions: $limlimits_{n rightarrow infty}{frac {2^{n+1}+3^{n+1}}{2^n + 3^n}} = 3$

How do I formally prove that $\lim\limits_{n \rightarrow \infty}{\frac {2^{n+1}+3^{n+1}}{2^n + 3^n}} = 3$. I calculated a few results so I am quite sure that the limit is $3$, but I'm struggling on how to do calculate/proof that correctly.

Answer

$$=\frac{2(\frac{2}{3})^n+3}{(\frac{2}{3})^n+1}$$