$3 \cdot 3$ Two positive numbers $m, n$ have a ratio of $t(t>1)$. If $m+n=s$, then the smaller of $m, n$ can be expressed as
(A) $t s$.
(B) $s-t s$.
(C) $\frac{t s}{1+s}$.
(D) $\frac{s}{1+t}$.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991)
[Solution] Given $m>0, n>0$, and $\frac{m}{n}=t>1$, we know that $n$ is smaller. Also, from $m+n=s$ we have $nt+n=s$, which gives $n=\frac{s}{1+t}$. Therefore, the answer is $(D)$.