To divide through by a function, is it required that the function being divided by is never 0?
$\displaystyle f(x)g(x) - f(x)h(x) = 0 \Rightarrow g(x) - h(x) = 0\ iff \ f(x) \neq 0$
Iff $\displaystyle f(x)\neq 0\;\forall x\in \textrm{Dom}(f)$ .
Regards.
Fernando Revilla