cocassi function algebra 2

Algebra Level 4

x,y,zx, y, z are non-zero real numbers such that:

x+y=4xy
y+z=6yz
z+x=8zx

If x+y+z=ab x+y+z = \frac{a}{b} where a,ba, b are positive coprime integers, what is a+b a + b ?

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