Question 108303
c=0, d=anything but 0, e=1, f=a+b. 

c=2, d=a+b, e=-1, f=a+b

c=1, d=1, e=1-a-b, f=a+b

Not very helpful I'm sure, but algebraically 1/(a+b) cannot be expanded into anything more helpful then it is. There are an infinite number of rational sums however.