If \(\frac{x}{2}+\frac{2}{y}=1\) and \(\frac{y}{2}+\frac{2}{z}=1\), then the value of \(\frac{z}{2}+\frac{2}{x}\) is:

From the first equation 2/y = (2 − x)/2, so y = 4/(2 − x). Then 2/z = 1 − y/2 = −x/(2 − x), so z/2 = −(2 − x)/x. Hence z/2 + 2/x = (x − 2 + 2)/x = 1.