已知:【(x方+y方)-(x-y)方+2y(x-y)】/4y=1,求4x/(4x方-y方)-1/(2x+y)的值
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已知:【(x方+y方)-(x-y)方+2y(x-y)】/4y=1,求4x/(4x方-y方)-1/(2x+y)的值
[(x²+y²)-(x-y)²+2y(x-y)]/4y=1
[x²+y²-(x²-2xy+y²)+2xy-2y²]/4y=1
(x²+y²-x²+2xy-y²+2xy-2y²)/4y=1
(4xy-2y²)/4y=1
2y(2x-y)/4y=1
(2x-y)/2=1
2x-y=2
4x/(4x²-y²)-1/(2x+y)
=4x/[(2x+y)(2x-y)]-(2x-y)/[(2x+y)(2x-y)]
=[4x-(2x-y)]/[(2x+y)(2x-y)]
=(4x-2x+y)/[(2x+y)(2x-y)]
=(2x+y)/[(2x+y)(2x-y)]
=1/(2x-y)
=1/2
[x²+y²-(x²-2xy+y²)+2xy-2y²]/4y=1
(x²+y²-x²+2xy-y²+2xy-2y²)/4y=1
(4xy-2y²)/4y=1
2y(2x-y)/4y=1
(2x-y)/2=1
2x-y=2
4x/(4x²-y²)-1/(2x+y)
=4x/[(2x+y)(2x-y)]-(2x-y)/[(2x+y)(2x-y)]
=[4x-(2x-y)]/[(2x+y)(2x-y)]
=(4x-2x+y)/[(2x+y)(2x-y)]
=(2x+y)/[(2x+y)(2x-y)]
=1/(2x-y)
=1/2
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