\(M=\frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c}\)
⇔\(M+3=\frac{b+c}{a}+1+\frac{c+a}{B}+1+\frac{a+b}{c}+1\)
⇔\(M+3=\frac{a+b+c}{a}+\frac{a+b+c}{b}+\frac{a+b+c}{c}\)
⇔\(M+3=abc\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
mà \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\)
⇔M+3=abc.0=0
⇔M=-3