2(x+y)=5(y+z)=3(z+x)
=> $\frac{2(x+y)}{30}$ = $\frac{5(y+z)}{30}$= $\frac{3(z+x)}{30}$
=> $\frac{x+y}{15}$ = $\frac{y+z}{6}$= $\frac{x+z}{10}$
Áp dụng TC dãy tỉ số bằng nhau
$\frac{x+y}{15}$ = $\frac{x+z}{10}$= $\frac{x+y- x- z}{15- 10}$= $\frac{y-z}{5}$
$\frac{x+z}{10}$ = $\frac{y+z}{6}$= $\frac{x+z- y-z}{10-6}$= $\frac{x-y}{4}$
=> $\frac{y-z}{5}$= $\frac{x-y}{4}$