Đề bài

Tính: a) \(\frac{1}{{ab}} + \frac{1}{{ac}} + \frac{1}{{bc}}\); b) \(\frac{{b - a}}{{ab}} + \frac{{c - b}}{{bc}} - \frac{{c - a}}{{ac}}\).

Lời giải chi tiết

a) \(\frac{1}{{ab}} + \frac{1}{{ac}} + \frac{1}{{bc}} = \frac{c}{{abc}} + \frac{b}{{abc}} + \frac{a}{{abc}} = \frac{{a + b + c}}{{abc}}\);b) \(\frac{{b - a}}{{ab}} + \frac{{c - b}}{{bc}} - \frac{{c - a}}{{ac}} = \frac{{c\left( {b - a} \right)}}{{abc}} + \frac{{a\left( {c - b} \right)}}{{abc}} - \frac{{b\left( {c - a} \right)}}{{abc}}\)

\( = \frac{{bc - ca - ab + ac - bc + ab}}{{abc}} = \frac{0}{{abc}} = 0\)