已知实数a满足a2+2a-8=0,求1a+1-a+3a2-1×a2-2a+1a2+4a+3的值.-数学

题目简介

已知实数a满足a2+2a-8=0,求1a+1-a+3a2-1×a2-2a+1a2+4a+3的值.-数学

题目详情

已知实数a满足a2+2a-8=0,求
1
a+1
-
a+3
a2-1
×
a2-2a+1
a2+4a+3
的值.
题型:解答题难度:中档来源:绵阳

答案

class="stub"1
a+1
-class="stub"a+3
a2-1
×
a2-2a+1
a2+4a+3

=class="stub"1
a+1
-class="stub"a+3
(a+1)(a-1)
×
(a-1)2
(a+3)(a+1)

=class="stub"1
a+1
-class="stub"a-1
(a+1)2

=
a+1-(a-1)
(a+1)2

=class="stub"2
(a+1)2

由a2+2a-8=0知,(a+1)2=9,
class="stub"2
(a+1)2
=class="stub"2
9

class="stub"1
a+1
-class="stub"a+3
a2-1
×
a2-2a+1
a2+4a+3
的值为class="stub"2
9

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