作业帮已知[(x²+y²)-(x-y)²+2y(x-y)]÷4y=1,求(4x/4x²-y²)-(1/2x+y)的值.
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已知[(x²+y²)-(x-y)²+2y(x-y)]÷4y=1,求(4x/4x²-y²)-(1/2x+y)的值.
已知[(x²+y²)-(x-y)²+2y(x-y)]÷4y=1,求(4x/4x²-y²)-(1/2x+y)的值.
已知[(x²+y²)-(x-y)²+2y(x-y)]÷4y=1,求(4x/4x²-y²)-(1/2x+y)的值.
分式有意义,y≠0
[(x²+y²)-(x-y)²+2y(x-y)]÷(4y)=1
x²+y²-(x²-2xy+y²)+(2xy-2y²)=4y
4xy-2y²=4y
2y²-4xy+4y=0
2y(y-2x+2)=0
y≠0,要等式成立,只有y-2x+2=0
2x-y=2
4x/(4x²-y²) - 1/(2x+y)
=4x/[(2x+y)(2x-y)]- 1/(2x+y)
=[4x-(2x-y)]/[(2x+y)(2x-y)]
=(2x+y)/[(2x+y)(2x-y)]
=1/(2x-y)
=1/2