# Beautiful But So Dangerous

Algebra Level 4

$\small \frac{x^3y^4z^3}{(x^4+y^4)(xy+z^2)^3}+\frac{y^3z^4x^3}{(y^4+z^4)(yz+x^2)^3}+\frac{z^3x^4y^3}{(z^4+x^4)(zx+y^2)^3}$

Over all positive reals $$x, y$$ and $$z$$, the maximum of the expression above can be expressed as $$\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers. Find $$m+n$$.

###### Source: VMO 2014 problem 2 day 2.
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