How to simplify this sum

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http://s1355.photobucket.com/user/deepan…

Let A = 4x^2 - 9y^2
B = 9y^2 - 16z^2
C = 16z^2 - 4x^2
A+B+C = 0
=>A^3 + B^3 + C^3 = 3ABC

Let D = 2x - 3y
E = 3y - 4z
F = 4z - 2x
D+E+F = 0
=>D^3 + E^3 + F^3 = 3DEF

We need to find
X = (A^3 + B^3 + C^3)/(D^3 + E^3 + F^3)
=3ABC/3DEF
=ABC/DEF

=(4x^2 - 9y^2)(9y^2 - 16z^2)(16z^2 - 4x^2)/
(2x - 3y)(3y - 4z)(4z - 2x)

=(2x+3y)(2x-3y)(3y+4z)*
(3y-4z)(4z+2x)(4z-2x)/
(2x - 3y)(3y - 4z)(4z - 2x)

=(2x+3y)(3y+4z)(4z+2x)