  Rao and Mitra in 1972 introduced two different types of constraints to extend
the concept of Bott-Duffin inverse and defined a new constrained inverse. Mary
in 2011 defined the inverse along an element that generalizes the Moore-Penrose
and Drazin inverses in a semigroup. Drazin in 2012 introduced the
$(b,c)$-inverse generalizing the Mary inverse. In 2017, Raki\'c noted that the
Rao-Mitra inverse is a direct precursor of the $(b,c)$-inverse. In this paper,
we introduce the notion of $EF$-inverse as a unified approach to the
aforementioned generalized inverses. Moreover, we show that the recently
introduced generalized bilateral inverses that in turn contain the OMP, MPO,
and MPOMP inverses can also be considered as special cases of the $EF$-inverse.
