If x + 1/y = 1, y + 1/z = 1, find the value of (z + 1/x ).

Let x = \(\frac{1}{2}\), y = 2 and z = -1

\(\frac{1}{2}\) + \(\frac{1}{2}\) = 1

2 - 1 = 1 (satisfied)

so, z + \(\frac{1}{x}\) = - 1 + 2 = 1