若xy=1,则1/(1+x^2)+1/(1+y^2)=?

Question

若xy=1,则1/(1+x^2)+1/(1+y^2)=?

Answer 1

解 1/(1+x^2)+1/(1+y^2)
=xy/[xy+x2]+xy/[xy+y2]
=xy/x[x+y]+xy/y[x+y]
=y/[x+y]+x/[x+y]
=[x+y]/[x+y]
=1