DÙng tính chất dãy tỉ số bằng nhau là ra nhé
\(\frac{a+b-c}{a}=\frac{a-b+c}{b}=\frac{-a+b+c}{c}=\frac{\left(a+b-c\right)+\left(a-b+c\right)+\left(-a+b+c\right)}{a+b+c}\)
\(=\frac{a+b-c+a-b+c-a+b+c}{a+b+c}=\frac{\left(a-a+a\right)-\left(c-c+c\right)+\left(b-b+b\right)}{a+b+c}=\frac{a+b+c}{a+b+c}=1\)
\(\Leftrightarrow a=b=c\)
\(\Rightarrow\)\(M=\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}=\frac{3.2a}{a^3}=\frac{6a}{a^3}=\frac{6}{a^2}\)