化简求值:先化简求值:(x2-16x2+8x+16+xx-4)÷1x2-16,其中x=2+1.-数学

题目简介

化简求值:先化简求值:(x2-16x2+8x+16+xx-4)÷1x2-16,其中x=2+1.-数学

题目详情

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
题型:解答题难度:中档来源:不详

答案

(
x2-16
x2+8x+16
+class="stub"x
x-4
)÷class="stub"1
x2-16

=[
(x+4)(x-4)
(x+4)2
+class="stub"x
x-4
]•(x+4)(x-4)
=[class="stub"x-4
x+4
+class="stub"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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