smc

We can write 2 equations. $\frac{x}{y}=\frac{a}{b}$ and $x+y=c$ Solving for $x$ and $y$ in terms of $a,b,c$ we get : $x=\frac{ac}{a+b}$ and $y=\frac{bc}{a+b}$ Since we know $a$ is less than $b$ and $\frac{x}{y}=\frac{bc}{a+b}$, the smaller of $x$ and $y$ must be $x$. Therefore the answer is $\boxed{\frac{ac}{a+b}}$.