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
问题描述：
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
答
[(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