$$ = \lim\_{x\to0} (\frac{e^x-1}{x} \* \frac{1}{x}) -\frac{x}{x^2}$$ 
$$ = \lim\_{x\to0} (\frac{e^x-1}{x} \* \frac{1}{x}) -\frac{x}{x^2}$$ 
$$ = 1 \* \lim\_{x\to0} \frac{1}{x} -\lim\_{x\to0}\frac{1}{x}$$
$$ = \infty -\infty$$

How do I actually solve this without using L'Hospital. I'm just looking for a hint, not a concrete answer.