Question

已知：x=1-

2

，y=1+

2

，求(

1

x+y

+

1

x-y

)÷

2x

x2-2xy+y2

的值．

Answer 1

原式=

x-y+x+y

(x-y)(x+y)

×

(x-y)2

2x

=

2x

(x-y)(x+y)

×

(x-y)2

2x

=

x-y

x+y

；
当x=1-

2

，y=1+

2

时，
原式=

1- 2 -1- 2

1- 2 +1+ 2

=

-2 2

2

=-

2

．