How do you express $1/(x^3-1)$ in partial fractions?

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Answer 1 · 2016-02-23T22:15:23

$1/(x^3-1)=(1/3)/(x-1)+(-1/3x-2/3)/(x^2+x+1)$

the factors of $(x^3-1)$ are $(x-1)$ and $(x^2+x+1)$

Set the equations using variables A, B, C so that

$1/(x^3-1)=A/(x-1)+(Bx+C)/(x^2+x+1)$

solve for the variables so that
$A=1/3$
$B=-1/3$
$C=-2/3$

God bless you ...

How do you express 1/(x^3-1)1/(x^3-1) in partial fractions?