已知实数满足a2+3a-2=0，求1a+1-a+2a2-1×a2-2a+1a2+4a+4的值．

题型：解答题难度：一般来源：不详

已知实数满足a²+3a-2=0，求

1

a+1

-

a+2

a2-1

×

a2-2a+1

a2+4a+4

的值．

答案

1

a+1

-

a+2

a2-1

×

a2-2a+1

a2+4a+4

=

1

a+1

-

a+2

(a-1)(a+1)

×

(a-1) 2

(a+2) 2

=

1

a+1

-

a-1

(a+1)(a+2)

=

a+2-a+1

(a+1)(a+2)

=

3

a 2+3a+2

∵a²+3a-2=0，
∴a²+3a=2，
∴原式=

3

2+2

=

3

4

．