Question

先化简，再求值：(

1

x-y

-

1

x+y

)÷

2y

x2-2xy+y2

，其中x=1+

2

，y=1-

2

．

Answer 1

原式=[

x+y

(x+y)(x-y)

-

x-y

(x+y)(x-y)

]÷

2y

(x-y)2

=

2y

(x+y)(x-y)

×

(x-y)2

2y

=

x-y

x+y

；
当x=1+

2

，y=1-

2

时，
原式=

1+ 2 -(1- 2 )

1+ 2 +1- 2

=

2

．