The first equation of the set

Algebra Level 2

Let x,y,zx,y,z be the real numbers such that xyz=1xyz=1. Find the value of

F=11+x+xy+11+y+yz+11+z+zx.F=\dfrac { 1 }{ 1+x+xy } +\dfrac { 1 }{ 1+y+yz } +\dfrac { 1 }{ 1+z+zx } .

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