Which expression is equivalent to the following complex fraction? $$ \frac{1-\frac{1}{x}}{2} $$

Question

UpStudy AI · Accepted Answer

Given the expression

$$
\frac{1-\frac{1}{x}}{2},
$$

we start by simplifying the numerator.

1. Combine the terms $$1$$ and $$-\frac{1}{x}$$:
   $$
   1-\frac{1}{x} = \frac{x}{x} - \frac{1}{x} = \frac{x-1}{x}.
   $$

2. Substitute the simplified numerator back into the original expression:
   $$
   \frac{\frac{x-1}{x}}{2}.
   $$

3. Simplify the complex fraction by multiplying by the reciprocal of $$2$$:
   $$
   \frac{x-1}{x} \times \frac{1}{2} = \frac{x-1}{2x}.
   $$

Thus, the expression is equivalent to

$$
\frac{x-1}{2x}.
$$
The expression is equivalent to $$ \frac{x-1}{2x} $$.

Which expression is equivalent to the following complex fraction? \( \frac{1-\frac{1}{x}}{2} \)