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1+x^3 = (1+x)(1-x+x^2)
let
3/(1+x^3) ≡ A/(1+x) + (Bx+C)/(1-x+x^2)
=>
3 ≡ A(1-x+x^2) + (Bx+C)(1+x)
x=-1, => A =1
coef. of x^2
A+B=0
B=-1
coef. of constant
A+C=3
C=2
3/(1+x^3) ≡ 1/(1+x) + (-x+2)/(1-x+x^2)
let
3/(1+x^3) ≡ A/(1+x) + (Bx+C)/(1-x+x^2)
=>
3 ≡ A(1-x+x^2) + (Bx+C)(1+x)
x=-1, => A =1
coef. of x^2
A+B=0
B=-1
coef. of constant
A+C=3
C=2
3/(1+x^3) ≡ 1/(1+x) + (-x+2)/(1-x+x^2)
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