  The fast diffusion equation $u_t=(u^{-1}u_x)_x$ is investigated from the
symmetry point of view in development of the paper by Gandarias [Phys. Lett. A
286 (2001) 153-160]. After studying equivalence of nonclassical symmetries with
respect to a transformation group, we completely classify the nonclassical
symmetries of the corresponding potential equation. As a result, new wide
classes of potential nonclassical symmetries of the fast diffusion equation are
obtained. The set of known exact non-Lie solutions are supplemented with the
similar ones. It is shown that all known non-Lie solutions of the fast
diffusion equation are exhausted by ones which can be constructed in a regular
way with the above potential nonclassical symmetries. Connection between
classes of nonclassical and potential nonclassical symmetries of the fast
diffusion equation is found.
