3. Suppose we have $\frac{r}{s}=\frac{t}{u}$, where both fractions are in lowest terms. Then, $ru=st$, which translates to $r|st$, $u|st$, $s|ru$, and $t|ru$. Since $\gcd(r,s)=\gcd(t,u)=1$, we must conclude that $r|t$, $u|s$, $s|u$, and $t|r$. This implies that $r=t$ and $s=u$.