  Structural and thermodynamic properties of multicomponent hard-sphere fluids
at odd dimensions have recently been derived in the framework of the rational
function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83},
011201 (2011)]. It is demonstrated here that the RFA technique yields the exact
solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ)
equation for binary mixtures at arbitrary odd dimensions. The proof relies
mainly on the Fourier transforms $\hat{c}_{ij}(k)$ of the direct correlation
functions defined by the OZ relation. From the analysis of the poles of
$\hat{c}_{ij}(k)$ we show that the direct correlation functions evaluated by
the RFA method vanish outside the hard core, as required by the PY theory.
