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

问题描述:

已知[(x2+y2)-(x-y)2+2y(x-y)]÷4y=1,求

4x
4x2y2
-
1
2x+y
的值.

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

1
2
y
∵x-
1
2
y=1,
∴2x-y=2,
4x
4x2y2
-
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