Solvable rational extensions of the Morse and Kepler-Coulomb potentials

We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using Darboux-B\"acklund transformations based on unphysical regular Riccati-Schr\"odinger functions which are obtained from specific symmetries associated to the considered family of potentials.