x²-4y²/x²+2xy+y²÷x+2y/2x²+2xy

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 08:45:20

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
(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)

原式=[(x+2y)(x-2y)/(x+y)²]÷[(x+2y)/2x(x+y)]
=[(x+2y)(x-2y)/(x+y)²][2x(x+y)/(x+2y)]
=2x(x-2y)/(x+y)
=(2x²-4xy)/(x+y)

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

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