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
的值. (a+1)(a+2)
a2−2a+1
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