  We show that every function in a reproducing kernel Hilbert space with a
normalized complete Pick kernel is the quotient of a multiplier and a cyclic
multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptano\u{g}lu. We
explore various consequences of this result regarding zero sets, spaces on
compact sets and Gleason parts. In particular, using a construction of Salas,
we exhibit a rotationally invariant complete Pick space of analytic functions
on the unit disc for which the corona theorem fails.
