Simplify:

$x - y - {x - y - (x + y) - ¯ ¯¯¯¯¯¯¯¯¯¯¯ ¯ x - y}$

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Solution

$x - y - {x - y - (x + y) - ¯ ¯¯¯¯¯¯¯¯¯¯¯ ¯ x - y} = x - y - {x - y - (x + y) - x + y} = x - y - {x - y - x - y - x + y} = x - y - x + y + x + y + x - y = 2 x$

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