Solution
= Solution
Take a reduced fraction $a/b\in R$. If $a\ne0$, its only possible inverse in $\mathbb Q$ is $b/a$. Since $\gcd(a,b)=1$, this is in lowest terms up to sign and belongs to $R$ exactly when $\gcd(a,30)=1$. Zero is not invertible. Therefore
$$
\boxed{R^\times=\{a/b:\gcd(a,b)=1,\ \gcd(ab,30)=1\}.}
$$
Equivalently, these are the <rational numbers> whose <valuations> at $2,3,5$ are all zero.