Let R, S, T, U be regexes.

Prove or disprove that :

        if S*(R + S) === R*(R + S)

           then, S* === R*

Please answer the question by the following format:
example:Let L be a language over Σ = {0, 1}, construct a DFSA that accepts it, as well as a regex that denotes it for the following language
L = {x ∈ Σ* : x ends in 01 or 10 or 00 or 11 }.
Answer:
DFSA: attatched

State Invariant(x, q0)

q0: iff x = ε

q1: iff x has one digit

q2: iff x ends with one of: 00, 01, 10, 11

regex: (0+1)*(0+1)(0+1)

This regex states that the string can have any number of 0s and 1s, as long as it ends with in 00, 01, 10, 11.