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We start from a seven parameters (six continuous and one discrete) family ofnon-central exactly solvable potential in three dimensions and construct a wideclass of ten parameters (six continuous and four discrete) family of rationallyextended exactly solvable non-central real as well as PT symmetric complexpotentials. The energy eigenvalues and the eigenfunctions of these extendednon-central potentials are obtained explicitly and it is shown that the waveeigenfunctions of these po- tentials are either associated with the exceptionalorthogonal polynomials (EOPs) or some type of new polynomials which can befurther re-expressed in terms of the corresponding classical orthogonalpolynomials. Similarly, we also construct a wide class of rationally extendedexactly solvable non-central real as well as complex PT-invariant potentials intwo dimensions.

A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions