Rule of de l'Hôpital (problem with reasoning)

[Function]

Hello everyone

 

My book gives us a proof for the rule of de l'Hôpital and to do this, its first statement is:

[math]\frac{f(x)}{g(x)}=\frac{f(x)-f(a)}{g(x)-g(a)}[/math]

 

However, I don't agree with this... Or I have no idea where that comes from... e.g.:

 

[math]f(x)=6x^3+2x^2+4[/math] and [math]g(x)=8x^2+3x+1[/math]

 

[math]\frac{f(3)}{g(3)}=2,243...\neq\frac{f(3)-f(7)}{g(3)-g(7)}=5,951...[/math]

 

What's wrong with this?

 

Thanks.

 

Function

Nope, wait.. I oversaw that [math]f(a)=g(a)=0[/math]

 

Sorry (...again..)

[mathematic]

Do you have a question? It looks like you figured it out.

[Function]

Not anymore, I edited it.. Sorry for waisting your time!