问题 填空题
设0<x<1,化简(
1+x
1+x
-
1-x
+
1-x
1-x2
+x-1
)(
1
x2
-1
-
1
x
)得______.
答案

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.

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