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