2012/028) If ab+ bc+ca = 1 Then show (a+b)/(1-ab) +( b+c)/(1-cb) + (c+a)/(1-ca) = 1/(abc)

ab + bc+ ca = 1

so bc + ca = 1- ab

or c(a+b) = (1- ab) or (a+b)/(1-ab) = 1/c

similarly (c+a)/(1-ac) = 1/b
and (b+c)/(1-bc) = 1/a

so (a+b)/(1-ab) + (b+c)/(1-cb) + (c+a)/(1-ca) = 1/c+ 1/a+ 1/b = (ab+bc+ca)/(abc) = 1/(abc)