Let $\displaystyle R$ and $\displaystyle S$ be the relations on z by defined by

$\displaystyle a R b \iff a \equiv b\mod 9$

$\displaystyle a S b \iff a \equiv b \mod 6$

Find $\displaystyle (RUS)^{\infty}$ and $\displaystyle \frac{A}{(RUS)^{\infty}}$