  Let $D$ be a closed disk in the complex plane centered at the origin, $f, g$
complex valued continuous function on $D$. Let $P[f,g; D]$ (res. $R[f, g; D])$)
be the uniform closure on $D$ of polynomials (res. rational functions) in
variables $f$ and $g$. In \cite{OS}, using complex dynamical systems, O'Farrell
and Sanabria-Garcia proved that $\{\Big(z^2, \cfrac{\overline
z}{1+\overline{z}}\Big): z\in D\}$ is not polynomially convex with $D$ small
enough and so that $P[z^2,\cfrac{\overline z}{1+\overline z}; D]\ne C(D)$ if
$D$ is sufficient small. In this paper, we first give a certain conditions for
rational convexity of union of two compact set of $\Bbb C^n$ and apply to show
that $R[z^2, \cfrac{\overline z}{1+\overline z}; D]= C(D)$ for all $D$ small
enough
