Question

设0＜x＜1，化简（

1+x

1+x - 1-x

+

1-x

1-x2 +x-1

）（

1 x2 -1

-

1

x

）得______．

Answer 1

原式=（

1+x

1+x - 1-x

+

1-x

1+x - 1-x

）（

1-x2

x

-

1

x

）
=

1+x + 1-x

1+x - 1-x

•

1-x2 -1

x

=

( 1+x + 1-x )2

(1+x)-(1-x)

•

1-x2 -1

x

=

2+2 1-x2

2x

•

1-x2 -1

x

=

(1-x2)-1

x2

=-1．
故本题答案为-1．