a^3 + b^3 = (a + b)(a^2 -  ab + b^2)

a^3 - b^3 = (a - b)(a^2  + ab + b^2)

a^-1 = 1/a

(a + b)/(a^1/3 + b^1/3) = (a^1/3 + b^1/3)(a^2/3 - a^1/3b^1/3+ b^2/3)/(a^1/3 + b^1/3) = a^2/3 - a^1/3b^1/3 + b^2/3

(a - b)/(a^1/3 - b^1/3) = (a^1/3 - b^1/3)(a^2/3 + a^1/3b^1/3+ b^2/3)/(a^1/3 - b^1/3) = a^2/3 + a^1/3b^1/3 + b^2/3

1/(a^2/3 + b^2/3)^-1 = a^2/3 + b^2/3

(a + b)/(a^1/3 + b^1/3) + (a - b)/(a^1/3 - b^1/3) - 1/(a^2/3 + b^2/3)^-1  =

a^2/3 - a^1/3b^1/3 + b^2/3 + a^2/3 + a^1/3b^1/3 + b^2/3 - a^2/3 - b^2/3 = a^2/3 + b^2/3

Verified answer

Ответ:

2-a^(2/3)-b^(2/3)

Объяснение: