Is the difference between two regular expressions a new regular expression? Let say the following:

Given Ax and Bx two literals which represent POSIX regular expressions.

Let def A as the set of literals that match Ax. The same def for B.

Using relative complement operation, is there always regular expression for $A/B$ set, for every pair of Ax,Bx? 

I attach an example:

Ax := a.*
Bx := a.*b$
// The difference A/B would be
Cx := a.*[^b]$
Regular languages are closed under relative complement. Since regular expressions encode exactly the regular languages, you can always find a regular expression that matches the relative complement of two other regular expressions.