  We consider the nonlinear Schr\"odinger equation in three space dimensions
with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in
the presence of an external inverse-square potential. We establish scattering
in the region of the mass-energy plane where the virial functional is
guaranteed to be positive. Our result parallels the scattering result of
\cite{R.Killip, T. Oh, O. Pocovnicu, and M. Visan} in the setting of the
standard cubic-quintic NLS.
