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.

问题描述:

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.

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