1 + a / (a - b) + 1 + b / (b - c) (b - a) + 1 + c / (c - a) (c - b)

1 + a / (a - b) + 1 + b / (b - c) (b - a) + 1 + c / (c - a) (c - b)

(1 + a) / (a - b) (a - c) + (1 + b) / (b - c) + (b - a) + (1 + c) / (c - a) (c - b)
= (1 + a) / (a - b) - (a - c) - (1 + b) / (b - c) (a - b) + (1 + c) / (a - c) (b - c)
= [(1 + a) (b - c) - (1 + b) (a - c) + (1 + c) (a - b)] / [a - b) (b - c) (a - c)] (통분)
= [b - c + ab - ac - a + c - ab + b + a - b + ac - bc] / [(a - b) (b - c) (a - c)]
= 0