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Some exactly solvable potentials in the position dependent mass backgroundare generated whose bound states are given in terms of Laguerre- or Jacobi-type$X_1$ exceptional orthogonal polynomials. These potentials are shown to beshape invariant and isospectral to the potentials whose bound state solutionsinvolve classical Laguerre or Jacobi polynomials.

Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schroedinger Hamiltonians