Given x / (2y) = 6 / 7, evaluate (x − y) / (x + y) + 14/19.

Introduction / Context:
We first transform the given ratio into a simple parametric form for x and y, then compute the target expression. This tests algebraic manipulation with ratios.

Given Data / Assumptions:
x/(2y) = 6/7 ⇒ x/y = 12/7.

Concept / Approach:
Parameterize x and y as a common multiple of the ratio, compute (x − y)/(x + y), and then add 14/19.

Step-by-Step Solution:
Let x = 12t and y = 7t. (x − y)/(x + y) = (12t − 7t)/(12t + 7t) = 5t/19t = 5/19. Add 14/19 ⇒ 5/19 + 14/19 = 19/19 = 1.

Verification / Alternative check:
Substitute t = 1: x = 12, y = 7 ⇒ (12 − 7)/(12 + 7) + 14/19 = 5/19 + 14/19 = 1.

Why Other Options Are Wrong:
5, 4, 3, 2 are not equal to the simplified sum; they ignore the fractional addition step.

Common Pitfalls:
Forgetting to reduce the fraction (x − y)/(x + y) properly or misadding numerator terms.

Final Answer:
1