Verified answer

a³ + b³ = (a + b)(a² - ab + b²)

(a^1/2)³ = a^3/2

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