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x²-4y²/x²+2xy+y²÷x+2y/2x²+2xy

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x²-4y²/x²+2xy+y²÷x+2y/2x²+2xy
x²-4y²/x²+2xy+y²÷x+2y/2x²+2xy
(x²-4y²)/(x²+2xy+y²)÷(x+2y)/(2x²+2xy)
=(x-2y)(x+2y)/(x+y)²÷(x+2y)/(2x²+2xy)
=(x-2y)(x+2y)/(x+y)²*(2x²+2xy)/(x+2y)
=(x-2y)/(x+y)²*(2x²+2xy)
=(x-2y)/(x+y)²*2x(x+y)
=(x-2y)/(x+y)*2x
=2x(x-2y)/(x+y)