All you had to do is ask!

They said, "Let S … be written as 1/P−1/Q". That simply means they want you to rewrite S in the form 1/P−1/Q. In other words, what do the polynomials P and Q need to be, so that:

1/P − 1/Q = 2x/(1 − x^2)

Yes, but note the grouping symbols added in red. (These are needed, when typing numerators or denominators that contain more than one term.)

Also, please use symbols

__as__ __given__: S, x, P, Q (not Sinf, X, p, q).

That's not a correct method for decomposition. Did you google for any lessons or examples, as suggested? (Maybe you're just guessing.)