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

(Crying)

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- Dec 2nd 2009, 06:32 AMxcludedpartial fraction did wrongly...
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

(Crying) - Dec 2nd 2009, 06:50 AMJester
- Dec 2nd 2009, 06:54 AMxcluded
- Dec 2nd 2009, 07:03 AMHallsofIvy
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.