问题 填空题
已知x=
2
+1
,则
x-2
x2-1
÷
2x+2
x2+2x+1
+
1
x-1
=______.
答案

x-2
x2-1
÷
2x+2
x2+2x+1
+
1
x-1

=

x-2
(x+1)(x-1)
×
(x+1) 2
2(x+1)
+
1
x+1

=

x-2
2(x-1)
+
2(x-1)
2(x+1)(x-1)

=

(x-2)(x-1)
2(x-1)(x+1)
+
2(x-1)
2(x+1)(x-1)

=

(x-2)(x-1)+2(x-1)
2(x-1)(x+1)

=

x
2(x+1)

x=

2
+1代入上式得:

原式=

2
+1
2(
2
+1+1)
=4
2

故答案为:4

2

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