A = a/(ab + a + 2) + b/(bc + b + 1) + 2c/(ac + 2c + 2)
= a/(ab + a + abc) + b/(bc + b + 1) + 2bc/(abc + 2bc + 2b)
= a/[a(b + 1 + bc)] + b/(bc + b + 1) + 2bc/(2 + 2bc + 2b)
= 1/(bc + b + 1) + b/(bc + b + 1) + bc/(bc + b + 1)
= (1 + b + bc)/(bc + b + 1) = 1