已知实数a满足a2+2a-8=0，则1a+1−a+3a

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已知实数a满足a²+2a-8=0，则

a+1

−

a+3

原式=
1
a+1-
a+3
(a+1)(a−1)•
(a−1)2
(a+1)(a+3)
=
1
a+1-
a−1
(a+1)2
=
a+1−(a−1)
(a+1)2
=
2
a2+2a+1，
∵a²+2a-8=0，
∴a²+2a=8，
∴原式=
2
8+1=
2
9．
故答案为
2
9．

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