How do I calculate/prove limits for exponential functions: $\lim\limits_{n \rightarrow \infty}{\frac {2^{n+1}+3^{n+1}}{2^n + 3^n}} = 3$ [duplicate]

Solution 1:

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