先化简,再求值:1/x+2−x2−4x+4x2−x÷(x+1−3/x−1),其中x满足x2+2x-4=0.

问题描述:

先化简,再求值:

1
x+2
x2−4x+4
x2−x
÷(x+1−
3
x−1
),其中x满足x2+2x-4=0.

原式=

1
x+2
(x−2)2
x(x−1)
÷
(x+1)(x−1)−3
x−1

=
1
x+2
(x−2)2
x(x−1)
x−1
(x+2)(x−2)

=
1
x+2
x−2
x(x+2)

=
2
x2+2x

由x2+2x-4=0,得x2+2x=4,
原式=
2
4
1
2