How can I show that $ \lim\limits_{x \rightarrow \infty} (1+ \frac{1}{4x^2 + 8/x})^{x^2+8/x} =e^\frac{1}{4} $ using that $ \lim\limits_{x \rightarrow \infty} (1+\frac{1}{x} ) ^x = e$ ?
I can obviously take out a 4 from the denominator, but how can I get the same power as what I'll get in the denominator?
Thanks in advance