Thank you for pointing that out. Let's re-evaluate the given expression step by step correctly.

The given expression is:

\[ \frac{1}{2 - \frac{1}{1 + \frac{1}{2}}} \]

First, let's simplify the innermost fraction:

\[ 1 + \frac{1}{2} = 1 + 0.5 = 1.5 = \frac{3}{2} \]

Now substitute this back into the expression:

\[ \frac{1}{2 - \frac{1}{\frac{3}{2}}} \]

Next, simplify the denominator:

\[ \frac{1}{\frac{3}{2}} = \frac{2}{3} \]

So, the expression becomes:

\[ \frac{1}{2 - \frac{2}{3}} \]

Now, subtract \(\frac{2}{3}\) from 2:

\[ 2 = \frac{6}{3} \]

\[ 2 - \frac{2}{3} = \frac{6}{3} - \frac{2}{3} = \frac{4}{3} \]

So, the expression now is:

\[ \frac{1}{\frac{4}{3}} \]

Finally, simplify the fraction:

\[ \frac{1}{\frac{4}{3}} = \frac{3}{4} \]

Thus, the simplified, reduced rational number is:

\[ \boxed{\frac{3}{4}} \]

Would you like more details or have any questions?

Here are 5 more questions you might be interested in:

1. How do you solve quadratic equations by factoring?
2. What is the process to find the derivative of a function?
3. How do you simplify complex fractions?
4. What are the steps to solve systems of equations using the substitution method?
5. How do you convert a repeating decimal into a fraction?

**Tip:** When simplifying complex fractions, always work from the innermost fraction outward, simplifying step by step.

Learn how to correctly simplify the fraction 1 / (2 - 1 / (1 + 1 / 2)) with a step-by-step solution. This problem involves nested fractions and simplification techniques. Suitable for students in Grades 7-9.

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