If x=a^2/3-a^-2/3 then find x^3 3x=?

Answer 1

let a^(2/3) = y for easier typing

then x = y - 1/y
= (y^2 - 1)/y

x^3 = (y^6 -3y^4 + 3y^2 - 1) / y^3
= (a^4 - 3a^(8/3) + 3a^(4/3) - 1)/a^2
or
a^2 - 3a^(2/3) + 3a^(-2/3) - a^-2

3x = 3a^(2/3) - 3a^(-2/3)