" (x) "(x^(3))/(y^(3))+(y^(3))/(z^(3))+(z^(3))/(x^(3))-3

x^(3)(y-z)^(3)+y^(3)(z-x)^(3)+z^(3)(x-y)^(3)

((x^(3)-y^(3))^(3)+(y^(3)-z^(3))^(3)+(z^(3)-x^(3))^(3))/((x-y)^(3)+(y-z)^(3)+(z-x)^(3))

x^(3)(y-z)^(3)+y^(3)(z-x)^(3)+z^(3)+z^(3)(x-y)^(3)

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)

(3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/ (1-3z^(2))=((3x-x^(3))/(1-3x^(2)))((3z-z^(3))/(1-3z^(2) ))(((3y-y^(3))/(1-3y^(2))))

(x-y)^(3)+(y-z)^(3)+(z-x)^(3)

If x + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

Simplify: ((x^(2)-y^(2))^(3) + (y^(2) - z^(2))^(3) + (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

Find ((x^(2)-y^(2))^(3) + (y^(2) -z^(2))^(3)+ (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

If x,y,z are different and Delta = {:|( x,x^(2) , 1+x^(3)),( y,y^(3) ,1+y^(3)),( z,z^(3) ,1+z^(3)) |:} then value of delta?