# Dividing through by functions

• November 19th 2010, 03:02 AM
mrmango
Dividing through by functions
To divide through by a function, is it required that the function being divided by is never 0?
$f(x)g(x) - f(x)h(x) = 0 \Rightarrow g(x) - h(x) = 0\ iff \ f(x) \neq 0$
• November 19th 2010, 03:18 AM
FernandoRevilla
Quote:

Originally Posted by mrmango
To divide through by a function, is it required that the function being divided by is never 0?
$f(x)g(x) - f(x)h(x) = 0 \Rightarrow g(x) - h(x) = 0\ iff \ f(x) \neq 0$

Iff $f(x)\neq 0\;\forall x\in \textrm{Dom}(f)$ .

Regards.

Fernando Revilla