Discussion
If two distinct non-zero real variables \(x\) and \(y\) are such that \((x + y)\) is proportional to \((x - y)\) then the value of \(\dfrac{x}{y}\)
Answer: D
The value of \(x/y\) is a constant.
Proportionality means \(x + y = k(x - y)\) for a fixed constant k. Rearranging:
\[ \begin{aligned} x + y &= kx - ky \\ y(1 + k) &= x(k - 1) \\ \frac{x}{y} &= \frac{k + 1}{k - 1} \end{aligned} \]
The right side involves only the constant k, so \(x/y\) is fixed and does not depend on x, on y, or on their product. (k cannot be 1, since that would force y = 0, and x and y are non-zero.)
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