Three ways to expand 1/(1+3x+2x^2) = 1/[(1+x)(1+2x)] = 2/(1+2x) - 1/(1+x)

(a) (1+y)^-1 where y=3x+2x^2

(b) 2(1+2x)^-1 - (1+x)^-1

(c) (1+x)^-1 * (1+2x)^ -1

These methods all give the correct polynomial.

Now with (b) and (c) the range of validity, -0.5<x<0.5 drops out clearly.

However, for (a) the range of validity is abs(y)<1 which gives a different set of values for x.

What is the resolution? Abandon method (a)? Why doesn't it work?

Any thoughts?!