"Spoooooooky" Russian rational expressions 26

Algebra Level 3

E=x2(xy)(xz)+y2(yx)(yz)+z2(zx)(zy) \mathscr{E} = \dfrac{x^2}{(x-y)(x-z)} + \dfrac{y^2}{(y-x)(y-z)} + \dfrac{z^2}{(z-x)(z-y)}

Let x=1008,y=2016,z=4032 x = 1008, y=2016, z = 4032 . Find the exact value of E \mathscr{E} .


Credit: My former Trig teacher's worksheet of Russian rational expressions
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