Hi pals , possible to check where did i went wrong ?
2 / s(1 + s^2) = A/s + B/(1 + s^2)
then , 2 = A(1 + s^2) + Bs
when s = 0 , A = 2
when s = 1 and A = 2 , B = -2
however i could not get B = -2s
Because the denominator is an "irreducible" (unfactorable in terms of real numbers) quadratic. If x- a is a factor of the denominator, the partial fractions expansion will include . If , so that it is irreducible, then the partial fractions expansion will include . If the denominator has as a factor, the partial fraction expansion will include . Finally, if the denominator has as a factor, the partial fraction expansion will include .
Since any polynomial, with real coefficients, can be factored (in the real numbers) to powers of linear or powers of quadratic terms, those are all the terms you need.