với a,b,c khác 0 ta có:\(\frac{ab}{a+b}=\frac{bc}{b+c}=\frac{ca}{c+a}\) => \(\frac{a+b}{ab}=\frac{b+c}{bc}=\frac{c+a}{ca}\)=>\(\frac{1}{b}+\frac{1}{a}=\frac{1}{c}+\frac{1}{b}=\frac{1}{a}+\frac{1}{c}\) =>\(\frac{1}{a}=\frac{1}{b}=\frac{1}{c}\) =>a=b=c => M=1