"Spoooooooky" Russian rational expressions 26

Algebra Level 3

\[ \mathscr{E} = \dfrac{x^2}{(x-y)(x-z)} + \dfrac{y^2}{(y-x)(y-z)} + \dfrac{z^2}{(z-x)(z-y)} \]

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


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