Question

已知实数a,b满足ab=1，求1/（a²+1）+1/（b²+1）的值

Answer 1

因为ab=1则1/（a²+1）+1/（b²+1）=ab/（a²+ab）+ab/（b²+ab）=（分别约掉a，b）b/（a+b）+a/（b+a）=(a+b)/（a+b)=1

Answer 2

ab=1，
1/(a²+1)+1/(b²+1)
=(b²+1)/(a²+1)(b²+1)+(a²+1)/(b²+1)(a²+1)
=(a²+1+1+b²+1)/(a²+1)(b²+1)
=(a²+2+b²)/(a²b²+a²+b²+1)
=(a²+2+b²)/(1+a²+b²+1)
=1