> 数学 >
已知实数a满足a2+2a-15=0,求
1
a+1
-
a+2
a2−1
÷
(a+1)(a+2)
a2−2a+1
的值.
人气:119 ℃ 时间:2019-08-22 14:01:07
解答
1
a+1
-
a+2
a2−1
÷
(a+1)(a+2)
a2−2a+1
=
1
a+1
-
a+2
(a+1)(a−1)
(a−1)2
(a+1)(a+2)
=
1
a+1
-
a−1
(a+1)2
=
2
(a+1)2

∵a2+2a-15=0,
∴(a+1)2=16,
∴原式=
2
16
=
1
8
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