The 100 followers problem!

Algebra Level 5

Given that

xy+yz+zx=0, \frac{ x}{y} + \frac{ y}{z} + \frac{ z}{x} = 0,

the value of

x14z7+y14x7+z14y7(x10z5+y10x5+z10y5)(x4z2+y4x2+z4y2)\frac{x^{14}z^7+y^{14}x^7+z^{14}y^7}{(x^{10}z^5+y^{10}x^5+z^{10}y^5)(x^{4}z^2+y^{4}x^2+z^{4}y^2)}

can be expressed as ab \frac a b for coprime positive integers. What is a+b a+ b ?

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