Let the first term of the geometric progression be a and the common ratio be r. Then, the sum of the first two terms is x = a + ar. The sum of the last two terms is y = ar^(n-2) + ar^(n-1). Dividing these two equations, we get:

\(\frac{y}{x}\) = \(\frac{ar^{n-2} + ar^{n-1}}{a + ar}\) = \(\frac{r^{n-2}(1 + r)}{1 + r}\) = \(r^{n-2}\)

Taking the \((n-2)\)-th root of both sides, we get:

\((\frac{y}{x})^{\frac{1}{n-2}}\) = \(r\)

Therefore, the common ratio of the geometric progression is \((\frac{y}{x})^{\frac{1}{n-2}}\). The correct answer is option D: \((\frac{y}{x})^{\frac{1}{n-2}}\).