Ta có :`a+b+c=2021`
`=>a=2021-b-c`
`=>b=2021-a-c`
`=>c=2021-a-b`
`=>C=c/(a+b)+a/(b+c)+b/(a+c)`
`=>C=(2021-a-b)/(a+b)+(2021-b-c)/(b+c)+(2021-a-c)/(a+c)`
`=>C=2021/(a+b)-(a+b)/(a+b)+2021/(b+c)-(b+c)/(b+c)+2021/(a+c)-(a+c)/(a+c)`
`=>C=2021/(a+b)+2021/(b+c)+2021/(a+c)-3`
`=>C=2021.(1/(a+b)+1/(b+c)+1/(a+c))-3`
`=>C=2021.1/90-3`
`=>C=2021/90-3`
`=>C=1751/90`
`=>` đpcm
$\text{Xin hay nhất }$