Question

已知x=

2

+1，y=

2

-1，试求

x2-y2

x2+2xy+y2

的值．

Answer 1

分析：此题化简原式后可得

x2-y2

x2+2xy+y2

=

(x+y)×(x-y)

(x+y)2

=

x-y

x+y

，代入即可．

解答：解：因为x=

2

+1，y=

2

-1，
所以

x2-y2

x2+2xy+y2

=

(x+y)×(x-y)

(x+y)2

=

x-y

x+y

=

2

2 2

=

2

2

．
所以答案为

2

2

．

点评：把原式化简后再代入，此题较为简单．