Đáp án:
$M=-3$
Giải thích các bước giải:
$\begin{array}{l}\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\\↔M=\dfrac{a+b}{c}+\dfrac{b+c}{a}+\dfrac{c+a}{b}\\↔M=\dfrac{a+b}{c}+1+\dfrac{b+c}{a}+1+\dfrac{c+a}{b}+1-3\\↔M=\dfrac{a+b+c}{c}+\dfrac{a+b+c}{a}+\dfrac{a+b+c}{b}-3\\↔M=(a+b+c)(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c})-3\\↔M=0-3=-3\\vậy M=-3\\\underline{\text{CHÚC BẠN HỌC TỐT}}\\\end{array}$