Question

化簡并求值：（

1

x-y

+

1

x+y

）÷

2x-y

x2-y2

，其中x，y滿足|x-2|+（2x-y-3）²=0．

Answer 1

（

1

x-y

+

1

x+y

）÷

2x-y

x2-y2

=

x+y+x-y

(x+y)(x-y)

•

(x+y)(x-y)

2x-y

=

2x

2x-y

，
∵|x-2|+（2x-y-3）²=0，
∴

x-2=0 2x-y-3=0

，
解得

x=2 y=1

．
∴原式=

2×2

2×2-1

=1

1

3

．