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

Solvable rational extensions of the Morse and Kepler-Coulomb potentials