Question

已知[(x²+y²)-(x-y)²+2y(x-y)]÷4y=1，求4x÷（4x²-y²）-1÷（2x+y）的值

球具体过程！

Answer 1

[(x²+y²)-(x-y)²+2y(x-y)]÷4y=1
(4xy-2y²)÷4y=1
得 2x-y=2
4x÷(4x²-y²)-1÷(2x+y)=4x÷[(2x-y)(2x+y)]-1÷(2x+y)
=2x÷(2x+y)-1÷(2x+y)
=(2x-1)/(2x+y)

Answer 2

[(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

x-1/2y=1
所以2x-y=2
4x÷（4x²-y²）-1÷（2x+y）

=4x/（4x²-y²）-(2x-y)/（4x²-y²）

=(4x-2x+y)/（4x²-y²）
=(2x+y)/(2x+y)(2x-y)
=1/(2x-y)
=1/2