# Proving that a certain limit involving exponentials exists and find its value

What is the best way to compute $$\lim_{x \to \infty} \frac{4^x+5^x}{4^{x+1}+5^{x+1}} \ ?$$ I have trouble working with exponential functions. My first guess was that the limit is 1, but then I looked up on Wolfram and it is not: the limit is $1/5$.

$$\frac{4^x+5^x}{4^{x+1}+5^{x+1}}=\frac{(\frac45)^x+1}{4(\frac45)^x+5}$$