Question

已知实数a满足a²+2a-8=0,求（a+1）分之1-（a²-1）分之（a+3）÷（a-1）分之（a+1）的值

Answer 1

a²+2a-8=0

(a+4)(a-2)=0

a1=-4 a2=2

（a+1）分之1-（a²-1）分之（a+3）÷（a-1）分之（a+1）

=（a+1）分之1-（a²-1）分之（a+3）×（a+1）分之（a-1）

=（a+1）分之1-（a+1）分之（a+3）×（a+1）分之1

=(a+1)²分之(a+1)-(a+1)²分之(a+3)

=(a+1)²分之(a+1-a-3)

=-(a+1)²分之2

a=4时

原式=-25分之2

a=-2时

原式=-2