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

．