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simplify 0.5x + 0.5 *x * (x * y - 1) / (y-1) + 0.5 * (1-x) * (x * y) /(y-1) = x
simplify 0.5x + 0.5 *x * (x * y - 1) / (y-1) + 0.5 * (1-x) * (x * y) /(y-1) = x
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