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[latex] \frac{x^2}{(x-y)(x-u)} + \frac{y^2}{(y-x)(y-u)} + \frac{u^2}{(u-x)(u-y)} =\\ \frac{x^2}{(x-y)(x-u)} + \frac{y^2}{(x-y)(u-y)} - \frac{u^2}{(x-u)(u-y)} =\\ \frac{x^2(u-y)}{(x-y)(x-u)(u-y)} + \frac{y^2(x-u)}{(x-y)(x-u)(u-y)} - \frac{u^2(x-y)}{(x-u)(x-y)(u-y)} =\\ \frac{x^2u-x^2y+xy^2-y^2u-xu^2+yu^2}{(x-u)(x-y)(u-y)} = \frac{x^2u-x^2y+xy^2-y^2u-xu^2+yu^2}{x^2u-x^2y+xy^2-y^2u-xu^2+yu^2} =1[/latex]