Question 2
Let $x$, $y$ and $z$ be positive real numbers. Find the maximum value of the following expression
$$
\frac{x^3 y^4 z^3}{(x^4 + y^4)(xy + z^2)^3} + \frac{y^3 z^4 x^3}{(y^4 + z^4)(yz + x^2)^3} + \frac{z^3 x^4 y^3}{(z^4 + x^4)(zx + y^2)^3}
$$
$$
\frac{x^3 y^4 z^3}{(x^4 + y^4)(xy + z^2)^3} + \frac{y^3 z^4 x^3}{(y^4 + z^4)(yz + x^2)^3} + \frac{z^3 x^4 y^3}{(z^4 + x^4)(zx + y^2)^3}
$$