`a+b+c=4`

`to (a+b+c)^2 = 4^2`

`a^2 +b^2 +c^2 + 2(ab+bc+ca) = 16`

`14 +2(ab+bc+ca) =16`

`2(ab+bc+ca)=2`

`ab+bc+ca=1`

`a+b+c=4`

`to {(a=4-b-c),(b=4-a-c),(c=4-a-b):}`

`M=1/(ab+c-3) +1/(bc+a-3)+1/(ca+b-3)`

`M=1/(ab +4-a-b-3) +1/(bc +4 -b-c-3) +1/(ca+4-a-c-3)`

`M=1/(a(b-1)-(b-1)) +1/(b(c-1) - (c-1)) +1/(a(c-1)-(c-1))`

`M=1/((a-1)(b-1)) +1/((b-1)(c-1)) +1/((c-1)(a-1))`

`M=(c-1 +a-1+b-1)/((a-1)(b-1)(c-1))`

`M=(a+b+c-3)/((a-1)(b-1)(c-1))`

`M=(4-3)/((a-1)(b-1)(c-1))`

`M=1/((a-1)(b-1)(c-1))`

Ta có `:`

`(a-1)(b-1)(c-1)=(ab-b-a+1)(c-1)`

`=abc - bc -ac +c -ab + b+a-1`

`=abc-(ab +bc+ca) + (a+b+c) -1`

`=-6 -1+4-1`

`=-4`

`to M=-1/4`