先化简,再求值:①2x+1-1x2-1÷xx2-2x+1,其中x=5;②(x-1x-x-2x+1)÷2x2-xx2+2x+1,其中x满足x2-x-1=0.-数学

题目简介

先化简,再求值:①2x+1-1x2-1÷xx2-2x+1,其中x=5;②(x-1x-x-2x+1)÷2x2-xx2+2x+1,其中x满足x2-x-1=0.-数学

题目详情

先化简,再求值:
2
x+1
-
1
x2-1
÷
x
x2-2x+1
,其中x=5;
(
x-1
x
-
x-2
x+1
2x2-x
x2+2x+1
,其中x满足x2-x-1=0.
题型:解答题难度:中档来源:不详

答案

①原式=class="stub"2
x+1
-class="stub"1
(x+1)(x-1)
(x-1)2
x

=class="stub"2
x+1
-class="stub"x-1
x(x+1)

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

=class="stub"x+1
x(x+1)

=class="stub"1
x

当x=5时,原式=class="stub"1
5


②原式=[
(x-1)(x+1)
x(x+1)
-
x(x-2)
x(x+1)
]•
(x+1)2
x(2x-1)

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

=class="stub"2x-1
x(x+1)
(x+1)2
x(2x-1)

=class="stub"x+1
x2

当x2-x-1=0时,x2=x+1,
则原式=1.

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