Olympiad corner #2

$Q1$ Find the largest y such that

$\frac { 1 }{ 1+{ x }^{ 2 } } \ge \frac { y-x }{ y+x } \quad for\quad all\quad x>0$

$Q2$ Find the minimum and maximum values of

$\frac { x+1 }{ xy+x+1 } +\frac { y+1 }{ yz+y+1 } +\frac { z+1 }{ zx+z+1 }$

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