  We show that a Lagrangian inclusion in $\mathbb C^2$ with double transverse
self-intersection points and standard open Whitney umbrellas is rationally
convex. As an application we show that any compact surface $S$, except $S^2$
and $\mathbb RP_2$, admits a pair of smooth complex-valued functions $f_1$,
$f_2$ with the property that any continuous complex valued function on $S$ is a
uniform limit of a sequence of $R_j(f_1,f_2)$, where $R_j(z_1,z_2)$ are
rational functions in $\mathbb C^2$.
