Question

How do you simplify `(x^2 - 1) / (1 -x^3)`?

Answer 1

Use the identity: a^3 - b^3 = (a - b)(a^2 + ab +b^2)

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

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