Applying replacement rules to products doesn't work as expected

Question

I have the following issue: I'd like to apply some replacement rules, for example

rules:={f[x]/t :> ff[x], g[x]/t :> gg[x]}

to an expression, e.g. like this:

(f[x]*g[x]/(t^2))/. rules

Surprisingly, this doesn't give the expected result

ff[x]*gg[x]

How do I fix this? Sorry if it's an easy question, I'm still a beginner with Mathematica.

Answer 1

The problem is that the forms f[x]/t and g[x]/t don't actually appear in the expression.

I try to keep the Left Hand Side of my rules as simple as possible. In this case I'd use

 rules = {f[x]->t ff[x], g[x] -> t gg[x]}