Đáp án:
\[M = 1\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
M = \frac{{3a}}{{ab + 3a + 6}} + \frac{{4b}}{{bc + 4b + 12}} + \frac{{2c}}{{ca + 2c + 8}}\\
= \frac{{3a}}{{ab + 3a + 6}} + \frac{{4ab}}{{abc + 4ab + 12a}} + \frac{{2abc}}{{{a^2}bc + 2abc + 8ab}}\\
= \frac{{3a}}{{ab + 3a + 6}} + \frac{{4ab}}{{24 + 4ab + 12a}} + \frac{{2.24}}{{24a + 2.24 + 8ab}}\\
= \frac{{3a}}{{ab + 3a + 6}} + \frac{{ab}}{{6 + ab + 3a}} + \frac{6}{{3a + 6 + ab}}\\
= \frac{{3a + ab + 6}}{{ab + 3a + 6}}\\
= 1
\end{array}\)
