$\dfrac{x + y}{z} = \dfrac{y + z}{x} = \dfrac{z + x}{y}$ is equal to :

1. 0

2. 1

3. 2

4. -2

Given,

$\dfrac{x + y}{z} = \dfrac{y + z}{x} = \dfrac{z + x}{y}$

Applying componendo on each side we get :

$\Rightarrow \dfrac{x + y}{z} + 1 = \dfrac{y + z}{x} + 1 = \dfrac{z + x}{y} + 1 \\[1em] \Rightarrow \dfrac{x + y + z}{z} = \dfrac{y + z + x}{x} = \dfrac{z + x + y}{y}.$

Since, above fractions are equal.

∴ We can conclude that,

x = y = z = a (let)

Substituting values of x, y and z in given equation we get :

$\Rightarrow \dfrac{x + y}{z} \\[1em] \Rightarrow \dfrac{a + a}{a} \\[1em] \Rightarrow \dfrac{2a}{a} \\[1em] \Rightarrow 2.$

Hence, Option 3 is the correct option.