  We introduce an operad of formal fractions, abstracted from the Mould operads
and containing both the Dendriform and the Tridendriform operads. We consider
the smallest set-operad contained in this operad and containing four specific
elements of arity two, corresponding to the generators and the associative
elements of the Dendriform and Tridendriform operads. We obtain a presentation
of this operad (by binary generators and quadratic relations) and an explicit
combinatorial description using a new kind of bi-colored trees. Similar results
are also presented for related symmetric operads.
