ab=1
1/(1+a²)+1/(1+b²)
=(b²+1+a²+1)/[(1+a²)(1+b²)]
=[(a+b)²-2ab+2]/(1+b²+a²+a²b²)
=[(a+b)²-2+2]/[1+(a+b)²-2ab+(ab)²]
=(a+b)²/[1+(a+b)²-2+(1)²]
=(a+b)²/(a+b)²
=1