If a, B and C are non-zero rational numbers, what is the value of AB / | ab | + BC / | BC | + AC / | AC |

If a, B and C are non-zero rational numbers, what is the value of AB / | ab | + BC / | BC | + AC / | AC |

When a, B and C are all negative or all positive, AB, BC and Ca are all positive, AB / | ab |, BC / | BC |, AC / | AC | are all 1,
ab/|ab| + bc/|bc| + ac/|ac| = 1+1+1 = 3
When a, B, C are two negative and one positive (or two positive and one negative), such as a < 0, B < 0, C > 0 (or a > 0, b > 0, C < 0), AB > 0, BC < 0, CA < 0, AB / | ab | = 1, BC / | BC | = - 1, AC / | AC | = - 1,
ab/|ab| + bc/|bc| + ac/|ac| = 1-1-1 = -1