The division problem in distribution theory.

Hi all.

Given a distribution v and a smooth f (both on a set X) - how do we find the distribution u such that fu = v? If f is never zero, then u = v/f is the solution.

I am trying to do the case where X is the real line and where f isn't always non zero.

The book I am reading tells me that if the points x in X such that f(x) = 0 are isolated zeros of finite order, then we can reduce to the case f(x) = x^m for some positive integer m.

Can anyone explain why this is true?

Thanks.