问题 解答题
化简求值:先化简求值:(
x2-16
x2+8x+16
+
x
x-4
1
x2-16
,其中x=
2
+1
答案

(

x2-16
x2+8x+16
+
x
x-4
1
x2-16

=[

(x+4)(x-4)
(x+4)2
+
x
x-4
]•(x+4)(x-4)

=[

x-4
x+4
+
x
x-4
]•(x+4)(x-4)

=(x-4)2+x(x+4)

=x2-8x+16+x2+4x

=2x2-4x+16

=2(x-1)2+14,

x=

2
+1时,

原式=2(

2
+1-1)2+14=18.

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