Fitting with functions as fit coefficients

Is it possible to fit a curve in IGOR, where two of the fit coefficients are functions of the independent variable?

For example, I have the fit equation:

f(x)=(C/x)*[a(x)/((b(x)+C)^2+2*a(x)^2)], C is some constant

I don't have equations for the fit coefficients a(x) and b(x), but want the fit to give me waves for both of them. 

Maybe I am approaching this incorrectly? Any help would be appreciated.

What you describe is not a well-defined fitting function. The fitting function must be evaluated at every value of the independent variable that appears in your input data. If you don't know the equations for a and b, then you can't do that.

Conceivably, you are working on some sort underdetermined inverse problem. Typically, such problems are solved by something like singular value decomposition, where the solution implies a constraint of the sort that makes the solution small in some sense. Igor curve fitting doesn't do that.