Don't understand how to simplify this limit

[zeion]

Homework Statement

lim
x->-1 x^1/3 + 1 / x + 1 = x^1/3 + 1 / x + 1 ((x^2/3 - x^1/3 + 1) / (x^2/3 - x^1/3 + 1))

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

cancel out and done


I don't understand how to know what reciprocal to multiply in cases like these to make it work.
Please help.

 

[Dick]

Your formatting is horrible. Use more parentheses, ok? I think you mean limit x->(-1) of (x^(1/3)+1)/(x+1). It might be a little clearer if you change variables first and let u=x^(1/3). So u->(-1) also and now your expression is (u+1)/(u^3+1). Can you factor (u^3+1)=(u+1)*(something)? Use polynomial division to divide u^3+1 by u+1 if you don't know the answer.