Question

已知实数a、b满足ab=1,那么1/（a*a+1）+1/（b*b+1)=?

Answer 1

1/（a*a+1）+1/（b*b+1)=（a*a+1+b*b+1)/（a*a+1）*（b*b+1)

=（a*a+b*b+2)/（a*a*b*b+a*a+b*b+1）=（a*a+b*b+2)/（ab*ab+a*a+b*b+1）

=（a*a+b*b+2)/（1+a*a+b*b+1）=1