Question

先化简，再求值：(

1

x-y

-

1

x+y

)÷

2y

x2+2xy+y2

，其中x=

3

+

2

，y=

3

-

2

．

Answer 1

(

1

x-y

-

1

x+y

)÷

2y

x2+2xy+y2

=

(x+y)-(x-y)

(x-y)(x+y)

•

(x+y)2

2y

=

2y

(x-y)(x+y)

•

(x+y)2

2y

=

x+y

x-y

，
把x=

3

+

2

，y=

3

-

2

代入上式，得
原式=

( 3 + 2 )+( 3 - 2 )

( 3 + 2 )-( 3 - 2 )

=

2 3

2 2

=

6

2

．