3√y - корень третьей степени из y
x^1/4 - x в степени 1/4
3√y^2 - корень третьей степени из у в степени 2
(√x-3√y^2) / (4√x - 3√y) + 3√y =
= (x^1/2-y^2/3) / (x^1/4 + y^1/3) + y^1/3=
= (x^1/2 - y^2/3 + y^1/3 * (x^1/4+y^1/3)) / (x^1/4 + y^1/3) =
= (x^1/2 - y^2/3 + y^1/3 * x^1/4 + y^1/3 * y^1/3) / (x^1/4 + y^1/3) =
= (x^1/4 * x^1/4 - y^1/3 * y^1/3 + y^1/3 * x^1/4 + y^1/3 * y^1/3) / (x^1/4 + y^1/3) =
= (x^1/4 * x^1/4 + y^1/3 * x^1/4) / (x^1/4 + y^1/3) =
= (x^1/4 * (x^1/4 + y^1/3)) / (x^1/4 + y^1/3) =
= x^1/4.
Ответ: x^1/4.