How to show R*S(U+TR*S)* is equivalent to (R+SU*T)SU*?

[PLAGUE]

TL;DR

How to show R*S(U+TR*S)* is equivalent to (R+SU*T)SU* using regular expression algebra?

I was studying the given finite automata. Using $$R_{ij}^{(k)}$$ method, I found out that the Regular Expression that this automaton accepts is $$R^*S(U+TR^*S)^*$$. But my book says, the regular expression for the accepted strings can be described
in various ways. One is $$(R+SU^*T)SU^*$$.

How do I show that these two regular expressions are equivalent?