Question

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

Answer 1

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

Explanation:

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 ...