Simplifying polynomial fractions with same `DiracDelta` function in both denominator and numerator

Question

I am trying to simplify an expression with multiple Diracdelta functions in both numerator and denominator. For example,

expr = (x1 DiracDelta[ω0 + ω]+x2 DiracDelta[ω0 + ω])/
        (x3 DiracDelta[ω0 + ω] - x4 DiracDelta[ω0 + ω]) // FullSimplify

However, DiracDelta[ω0 + ω] does not cancel out during the simplification. I have already read answers to this, this, and this questions, and I understand that this is due to the definition of DiracDelta[ω0 + ω].

This is my approach:

expr /.{DiracDelta[ω0 + ω]->X}// FullSimplify

It works, however, not very convenient for complicated expressions with multiple DiracDelta at different values.

Is there any better approach to cancel out same DiracDelta functions both denominator and numerator?

Answer 1

Answer instead of comment.

Use //Factor instead of //FullSimplify

Answer 2

Try this:

expr = (x1 DiracDelta[ω0 + ω] + x2 DiracDelta[ω0 + ω])/(x3 DiracDelta[ω0 + \
ω] - x4 DiracDelta[ω0 + ω]) // Cancel

(* (x1 + x2)/(x3 - x4)  *)

Have fun!