Given is that $x, y, z$ are real numbers, different from 0, $x$ and $z$ are different, such that $(x+y) ^2+(2-xy)=9$ and $(y+z) ^2-(3+yz)=4$ Find the value of $A=(x/y+y^2/x^2+z^3/x^2y)(y/z+z^2/y^2+x^3/y^2z)(z/x+x^2/z^2+y^3/z^2x)=?$
Source: Greece Archimedes Junior 2016
Tags: algebra
Given is that $x, y, z$ are real numbers, different from 0, $x$ and $z$ are different, such that $(x+y) ^2+(2-xy)=9$ and $(y+z) ^2-(3+yz)=4$ Find the value of $A=(x/y+y^2/x^2+z^3/x^2y)(y/z+z^2/y^2+x^3/y^2z)(z/x+x^2/z^2+y^3/z^2x)=?$