Question
Which expression is equivalent to the following complex fraction? \( \frac{1-\frac{1}{x}}{2} \)
Ask by Ward Morrison.
Mar 11,2025 01:11
UpStudy AI Solution
Tutor-Verified Answer
Answer
The expression is equivalent to \( \frac{x-1}{2x} \).
Solution
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The Deep Dive
To simplify the complex fraction \( \frac{1-\frac{1}{x}}{2} \), start by focusing on the numerator. The expression within the numerator can be combined into a single fraction. This gives us:
\( 1 - \frac{1}{x} = \frac{x - 1}{x} \).
Now we substitute this back into the complex fraction:
\( \frac{\frac{x - 1}{x}}{2} \).
This simplifies to:
\( \frac{x - 1}{2x} \).
So the equivalent expression is \( \frac{x - 1}{2x} \).
Now you’re ready to solve it like a pro! Keep practicing those fractions, because when you simplify them correctly, a world of mathematical possibilities opens up!
Want to dig deeper? Check out how combining fractions in different forms can unveil their beauty in both algebra and real-world problems, such as calculating rates or adjusting recipes!
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