In this paper we discuss convergence properties and error estimates of rational
Bernstein operators introduced by P. Pit¸ul and P. Sablonni`ere. It is shown that the
rational Bernstein operators converge to the identity operator if and only if the maximal
difference between two consecutive nodes is converging to zero. Further a Voronovskaja
theorem is given based on the explicit computation of higher order moments for the
rational Bernstein operator
