已知a2+2a=8,则1a+1-1a2-1÷a+1a2-2a+1的值为______.-数学

题目简介

已知a2+2a=8,则1a+1-1a2-1÷a+1a2-2a+1的值为______.-数学

题目详情

已知a2+2a=8,则
1
a+1
-
1
a2-1
÷
a+1
a2-2a+1
的值为______.
题型:填空题难度:偏易来源:不详

答案

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

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

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

∵a2+2a=8,
∴(a-2)(a+4)=0,解得a1=2,a2=-4,
当a=2时,原式=class="stub"2
(2+1)2
=class="stub"2
9

当a=-4时,原式=class="stub"2
(-4+1)2
=class="stub"2
9

故答案为:class="stub"2
9

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