$\\$
`13/(x+y) +(13)/(y+z) + (13)/(z+x) = 143/10`
`-> 13 (1/(x+y)+1/(y+z) +1/(z+x) ) = 143/10`
`-> 1/(x+y)+1/(y+z)+1/(z+x)=143/10 : 13`
`-> 1/(x+y)+1/(y+z)+1/(z+x)=11/10`
$\\$
`(11z)/(x+y)+(11x)/(y+z)+(11y)/(z+x)=143/10`
`-> ( (11z)/(x+y)+(11x)/(y+z)+(11y)/(z+x) ) . 1/11= 143/10 . 1/11`
`-> z/(x+y)+x/(y+z)+y/(z+x) = 13/10`
`-> z/(x+y)+x/(y+z)+y/(z+x) +3=13/10 + 3`
`-> ( z/(x+y)+1) + ( x/(y+z)+1) + (y/(z+x)+1)=43/10`
`-> ( z/(x+y)+(x+y)/(x+y) ) + (x/(y+z)+(y+z)/(y+z) ) + (y/(z+x)+(z+x)/(z+x) ) = 43/10`
`->(x+y+z)/(x+y) + (x+y+z)/(y+z) + (x+y+z)/(z+x) = 43/10`
`-> (x+y+z) (1/(x+y)+1/(y+z)+1/(z+x) ) = 43/10`
`-> (x+y+z) . 11/10 = 43/10`
`-> x+y+z=43/10 : 11/10`
`->x+y+z=43/11`
Vậy `x+y+z=43/11`
