proving the independance of an equation, from certain variables

by kenith   Last Updated April 15, 2019 10:20 AM

The different and unequal to zero real numbers x, y, z satisfy the equation

$$x^3+y^3+m(x+y)=y^3+z^3+m(y+z)=z^3+x^3+m(z+x)$$

prove that

$$K=(\frac{x-y}{z}$$ $$+\frac{y-z}{x}$$ $$+\frac{z-x}{y})$$ $$(\frac{z}{x-y}$$ $$+\frac{x}{y-z}$$ $$+\frac{y}{z-x})$$ is not dependnent upon $$x, y, z, m$$

I don't know how to solve the question above. I've been trying it for a while, but I can't. Can you guys please help me?

Kevin

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