先化简,再求值:(x+2/x2-2x-x-1/x2-4x+4)÷x2-16x2+4x,其中x=2+3.
问题描述:
先化简,再求值:(
-x+2
x2-2x
)÷x-1
x2-4x+4
,其中x=2+
x2-16
x2+4x
.
3
答
原式=[
-x+2 x(x-2)
]÷x-1 (x-2)2
x2-16
x2+4x
=[
-
x2-4 x(x-2)2
]÷
x2-x x(x-2)2
x2-16
x2+4x
=
•x-4 x(x-2)2
x(x+4) (x+4)(x-4)
=
,1 (x-2)2
当x=2+
时,
3
原式=
1 (2+
-2)2
3
=
.1 3