Patrick F. answered • 09/30/15

Tutor

4.6
(49)
Tutoring in Physics, chemistry, any level of math

To help make things a bit cleaner, I will define t

^{1/3}= x and a^{1/3}= y. thus, the expression is(x

^{2}- y^{2}) / (x^{3}- y^{3})Factor: the numerator is (x - y)(x + y), and the denominator is (x- y)(x

^{2}+ xy + y^{2}). This becomes(x + y) / (x

^{2}+ xy + y^{2}) = (t^{1/3}+ a^{1/3}) / (t^{2/3}+ (ta)^{1/3}+ a^{2/3})In the limit t --> a, we have

(2a

^{1/3}) / (3a^{2/3}) = 2 / (3a^{1/3})