I have the following limit:
$ \lim_{x\to \infty}{\bigg( \frac{x^2 + 3x - 1}{x^2 + 3} \bigg) }^\frac{x -2}{2} $ We had no explanations for calculating such limits i looked over few poor textbook examples and i understand the result of this limit will be $ e^X $ where X will be what i get from expanding the limits $ \frac {x-2}{2} $.
And that first step is to get the following form:
$ \lim_{x\to\infty}{ \bigg ( 1 + \frac{1}{x+1} \bigg )^{x+1} } = e $
Are there any simpler steps to solving such a limit ?