To evaluate the limit as x approaches a for the expression (x^(1/3) - a^(1/3))/(x - a), it's essential to factor out (x - a) from the numerator. This can be achieved using the identity for the difference of cubes, where A = x^(1/3) and B = a^(1/3), leading to the factorization (x - a) = (x^(1/3) - a^(1/3))(x^(2/3) + a^(1/3)x^(1/3) + a^(2/3)). Alternatively, one can rationalize the numerator by multiplying both the numerator and denominator by the conjugate, which also simplifies the limit evaluation. This approach allows the limit to be computed without the denominator equating to zero.