已知x=2+1，则x-2x2-1÷2x+2x2+2x+1+1x-1=______．

题型：填空题难度：一般来源：不详

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)

，
把x=

2

+1代入上式得：
原式=

2 +1

2( 2 +1+1)

=4

2

，
故答案为：4

2

．