先化简,再求值:(1-3x+2)÷x?1x2+2x-xx+1,其中x满足x2-x-1=0

先化简,再求值:(1-3x+2)÷x?1x2+2x-xx+1,其中x满足x2-x-1=0.
2025-06-01 04:22:11
推荐回答(2个)
回答1:

原式=

x+2?3
x+2
?
x(x+2)
x?1
-
x
x+1
=
x?1
x+2
?
x(x+2)
x?1
-
x
x+1
=x-
x
x+1
=
x2
x+1

∵x2-x-1=0,∴x2=x+1,
则原式=1.

回答2:

解:(1-3x+2)÷x-1x2+2x-xx+1=(x+2x+2-3x+2)×x(x+1)x-1-xx+1=x-1x+2×x(x+2)x-1-xx+1=x2x+1,
由x2+x-2=0,得x1=1,x2=-2 (舍去),
则原式=x2x+1=12.