Limit problem

Question

How do you find the limit of (x^2/3-1) / (x-1) as x approaches 1.

Answer 1

factoring is the key to this one.

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

and denominator can also be factored [difference of cubes]: (x^1/3-1)(x^2/3+x^1/3+1)

 

and after cancellation of identical factors, the rational no longer has problems and direct substitution is indicated.

 

Answer: 2/3 (two thirds)