I know how to use numapprox to fit polynomial and rational polynomial approximations to trig functions.  I would like to fit a rational expression using numerators and denominators like this:

a*x^(1/3) + b*x^(1/2) + c*x^(2/3) + d*x + e*x^(3/2) + f*x^(2) + g*x^(3)