A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46-54]

•The equivalence of two conditions on SI rationally extended potentials is established.•The identification works for exceptional X1 and Xℓ Laguerre or Jacobi cases.•The link between shape invariance and potential algebra is strengthened.

It is proved the equivalence of the compatibility condition of Ramos (2011, 2012) with a condition found in Yadav et al. (2015). The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xℓ Jacobi and Laguerre cases are given.