Consider the sequence x[n] for which the z-transform is x(z) = (1/3)/(1-(1/2)z^(-1)) + (1/4)/(1-2z^(-1)), and the ROC includes the unit circle. Determine x[0] using the initial value. Which of the following options correctly calculates x[0]?

A) x[0] = (1/3) + (1/4)
B) x[0] = (1/3) - (1/4)
C) x[0] = (1/3) + (1/2)
D) x[0] = (1/3) - (1/2)