Understanding formal statement of L'hospital's Rule

The Statement of L'hospital's Rule given on my book goes like this-

"**Let f and g be two real valued functions differentiable at each point x in $\displaystyle (a-\delta,a+\delta),$and g'(x) is not equal to 0 for all x such that $\displaystyle **

0<\mid x-a\mid <\delta

$.

**If $\displaystyle \lim_{x\rightarrow a} f'(x)/g'(x)$exists and $\displaystyle \lim_{x\rightarrow a} f(x)=0=\lim_{x\rightarrow a} g(x)$,then $\displaystyle \lim_{x\rightarrow a} f(x)/g(x)$ also exists and $\displaystyle \lim_{x\rightarrow a} f(x)/g(x)$=$\displaystyle \lim_{x\rightarrow a} f'(x)/g'(x)$ **