To determine which expression is equivalent to the given complex fraction [tex]\(\frac{1 - \frac{1}{x}}{2}\)[/tex], we will simplify the expression step-by-step.
First, let's rewrite the numerator of the complex fraction:
[tex]\[
1 - \frac{1}{x}
\][/tex]
To combine the terms in the numerator, we need a common denominator:
[tex]\[
1 = \frac{x}{x}
\][/tex]
This allows us to write the numerator as:
[tex]\[
1 - \frac{1}{x} = \frac{x}{x} - \frac{1}{x} = \frac{x - 1}{x}
\][/tex]
Now the original complex fraction can be rewritten as:
[tex]\[
\frac{\frac{x - 1}{x}}{2}
\][/tex]
Next, we simplify the division of fractions by multiplying by the reciprocal of the denominator:
[tex]\[
\frac{\frac{x - 1}{x}}{2} = \frac{x - 1}{x} \times \frac{1}{2} = \frac{(x - 1) \cdot 1}{2 \cdot x} = \frac{x - 1}{2x}
\][/tex]
Thus, the expression [tex]\(\frac{1 - \frac{1}{x}}{2}\)[/tex] is equivalent to:
[tex]\[
\frac{x - 1}{2x}
\][/tex]
Therefore, the correct option is:
[tex]\[
\boxed{\frac{x-1}{2 x}}
\][/tex]
