How to solve this limit without (L'Hôpital's rule) I need to solve this limit without L'Hôpital's rule. These questions always seem to have some algebraic trick which I just can't see this time.
$$ \bbox[yellow]
{
\lim_{x\to 2} \left( \frac{e^2-e^x} {2-x}  \right)
}
$$
Could someone give me a hint as to what I need to do to the fraction to make this work? Thanks!

The expression is the definition of the derivative of $e^x$ evaluated at $x=2$.  It does not require L'Hopital to conclude that the limit is $e^2$.
