Find $f(x)$ concave and $g(y)$ convex such that $f(x)/g(y)$ is convex

Question

I'm looking for two functions $f(x)$ concave and $g(y)$ convex such that their ratio $h(x,y)=f(x)/g(y)$ is convex. Both $f$ and $g$ cannot be constant. Their domain of definition can be $R$ or any subset of $R$. Ideally, their image would include at least part of $R_+$. Any help is much appreciated!