The line segment is given and points $A,B,C,D$ are marked on the line segment(endpoints of it are A,D respectively and $ B < C $) .
So there are $3$ segments at the line segment and We know the $2$ following ratios.
$AC:CD=1:s$
$AB:BD=t:1$
$s,t > 0$
From above ratios,the $AB:BC:CD$ is equal to $\displaystyle\frac{t}{1+t}:1-\displaystyle\frac{s}{1+s}-\displaystyle\frac{t}{1+t}:\frac{s}{1+s}$ $\quad $.
How do I deduce it?.
Suppose the length $AD$ is $L$. Then $AB=\frac{t}{1+t}L$ and $CD=\frac{s}{1+s}L$, so $BC=L-AB-CD=L-\frac{t}{1+t}L-\frac{s}{1+s}L$. Hence the ratio is $$AB:BC:CD=\frac{t}{1+t}:1-\frac{t}{1+t}-\frac{s}{1+s}:\frac{s}{1+s}$$