CM: `1<a/(a+b)+b/(b+c)+c/(c+a)<2`
Ta có : `a/(a+b+c)<a/(a+b)<(a+c)/(a+b+c)`
`b/(b+c+a)<b/(b+c)<(b+a)/(b+c+a)`
`c/(c+a+b)<c/(c+a)<(c+b)/(c+a+b) `
`=>a/(a+b+c)+b/(a+b+c)+c/(a+b+c) < a/(a+b) +b/(b+c) +c/(c+a)`
`=>a/(a+b)+b/(b+c)+c/(c+a)<(a+c)/(a+b+c)+(b+a)/(b+c+a)+(c+b)/(c+a+b) `
`=>(a+b+c)/(a+b+c)<a/(a+b)+b/(b+c)+c/(c+a)<(a+b+b+a+c+c)/(a+b+c)`
`=>1<a/(a+b)+b/(b+c)+c/(c+a)<2.(a+b+c)/(a+b+c)`
`=>1<a/(a+b)+b/(b+c)+c/(c+a)<2`
`=>đpcm`
$\text{Xin hay nhất }$