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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 $1/5$.

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

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