Đáp án:
\[0\]
Giải thích các bước giải:
\[\begin{array}{l}
\frac{a}{{\left( {a - b} \right)\left( {a - c} \right)}} + \frac{b}{{\left( {b - a} \right)\left( {b - c} \right)}} + \frac{c}{{\left( {c - a} \right)\left( {c - b} \right)}}\\
= \frac{{a\left( {b - c} \right)}}{{\left( {a - b} \right)\left( {a - c} \right)\left( {b - c} \right)}} + \frac{{b\left( {c - a} \right)}}{{\left( {b - a} \right)\left( {b - c} \right)\left( {c - a} \right)}} + \frac{{c\left( {a - b} \right)}}{{\left( {c - a} \right)\left( {c - b} \right)\left( {a - b} \right)}}\\
= \frac{{ab - ac}}{{\left( {a - b} \right)\left( {a - c} \right)\left( {b - c} \right)}} + \frac{{bc - ba}}{{\left( {a - b} \right)\left( {b - c} \right)\left( {a - c} \right)}} + \frac{{ca - cb}}{{\left( {a - c} \right)\left( {b - c} \right)\left( {a - b} \right)}}\\
= \frac{{ab - ac + bc - ba + ca - cb}}{{\left( {a - b} \right)\left( {a - c} \right)\left( {b - c} \right)}}\\
= \frac{0}{{\left( {a - b} \right)\left( {a - c} \right)\left( {b - c} \right)}} = 0
\end{array}\]
