Please help me solve this...Thanks in advance

Question

Solve for x: ((2x(x^2-x)^(-1/3))(2x-1) / (3)) + ((x^2-x)^(2/3)) = 0 (where x not equal to 0)

Answer 1

Let y=(x^2-x)^1/3: 2x(2x-1)/(3y)+y^2=0 (this step is for convenience);

2x(2x-1)+3y^3=0; 4x^2-2x=-3y^3=-3(x^2-x)=-3x^2+3x

7x^2-5x=0; x(7x-5)=0; x=5/7 because x not zero.