已知实数a,b满足ab=1,那么1/(a2+1)+1/(b2+1)=?(用通分)

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已知实数a,b满足ab=1,那么1/(a2+1)+1/(b2+1)=?(用通分)已知实数a,b满足ab=1,那么1/(a2+1)+1/(b2+1)=?(用通分)已知实数a,b满足ab=1,那么1/(a

已知实数a,b满足ab=1,那么1/(a2+1)+1/(b2+1)=?(用通分)
已知实数a,b满足ab=1,那么1/(a2+1)+1/(b2+1)=?(用通分)

已知实数a,b满足ab=1,那么1/(a2+1)+1/(b2+1)=?(用通分)
1/(a²+1)+1/(b²+1)
=1/(a²+ab)+1/(b²+ab)
=1/a(a+b) +1/b(a+b)
=b/ab(a+b) + a/ab(a+b)
=(a+b)/ab(a+b)
=1/ab
=1

ab=1,
1/(a2+1)+1/(b2+1)
=(a²+b²+2)/(a²+1)(b²+1)
=(a²+b²+2)/(a²b²+a²+b²+2)
=(a²+b²+2)/(a²+b²+3)
=1-1/(a²+b²+3)