If two distinct non-zero real variables $x$ and $y$ are such that $(x + y)$ is proportional to $(x - y)$ then the value of $\frac{x}{y}$

Given that $(x + y)$ is directly proportional to $(x - y)$:

where $k$ is a non-zero proportionality constant ($k \neq 1$, since $y \neq 0$).

Rearranging the terms:

Dividing both sides by $y(k - 1)$ (since $x$ and $y$ are distinct, $x - y \neq 0 \implies k \neq 1$):

Since $k$ is a fixed constant, $\frac{1 + k}{k - 1}$ is also a fixed constant.

Therefore, the value of $\frac{x}{y}$ is a constant.

Hence, D is the correct option.