I don't understand this question. I am suppose to be simplifying this:

Question

u^4-1/u^3-1

I put (u^2+1) (u+1)(u-1) for the top but the bottom, I can't figure out why my book put (u^2+u+1)(u-1) when it's only u^3...where did the extra u come from?

Answer 1

u^4 - 1 = (u^2-1)(u^2+1) = (u-1)(u+1)(u^2+1)

u^3 - 1 = (u-1)(u^2+u+1)

divide to get

(u+1)(u^2+1)/(u^2+u+1)