abc = 13
(a + 1/b)(b + 1/c)(c + 1/a) = (1 + 1/a)(1 + 1/b)(1 + 1/c)
(ab + 1)(bc + 1)(ca + 1) = (a + 1)(b + 1)(c + 1)
(abc)^2 + abc × (a + b + c) + (ab + bc + ca) + 1
= abc + (ab + bc + ca) + (a + b + c) + 1
(a + b + c) × (13 — 1) = 13 — 13^2
Answer, a + b + c
= 13 × (1 — 13) / (13 — 1)
a + b + c = –13