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(1/y - 1/(1/y)) (y-1/y) =
(1/y - y) (y - 1/y) =
-1(y - 1/y) (y - 1/y) =
-1(y - 1/y)² =
-1(y² - 2/y - 1/y²) =
-y² + 2/y + 1/y²