If x, y, z are three numbers such that $x+y=13, y+z=15$ and $z+x=16$, the value of $\frac{x y+x z}{x y z}$ is:

$\frac{5}{18}$

$x+y=13, y+z=15$ and $z+x=16$

By adding all of these we get,

x + y + y + z + z + x = 13 + 15 + 16

2(x + y + z) = 44

x + y + z = 22

x = 22 - 15 = 7

y = 22 - 16 = 6

x = 22 - 13 = 9

The value of $\frac{x y+x z}{x y z}$ = $\frac{7 × 6+7 × 9}{7 × 6 × 9}$

The value of $\frac{x y+x z}{x y z}$ = $\frac{105}{378}$

The value of $\frac{x y+x z}{x y z}$ = $\frac{5}{18}$