It looks like you're trying to represent a mathematical expression, but it's incomplete. Let me attempt to interpret it. Based on the way it's written, I think you mean:

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

If this interpretation is correct, we can now solve this expression.

### Step 1: Simplify the denominator
The denominator is \( 3 + \frac{1}{4} \), which can be written as a fraction:

\[
3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}
\]

### Step 2: Rewrite the expression
Now the entire expression becomes:

\[
\frac{1}{\frac{13}{4}}
\]

### Step 3: Simplify
Dividing by a fraction is equivalent to multiplying by its reciprocal:

\[
\frac{1}{\frac{13}{4}} = \frac{4}{13}
\]

### Final Answer:
\[
\frac{4}{13}
\]

Would you like further details or explanations?

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Here are 5 related questions:
1. How do you simplify complex fractions?
2. What happens when you add two fractions with different denominators?
3. How do you convert a mixed number into an improper fraction?
4. How do you divide fractions?
5. What is the reciprocal of a fraction?

**Tip:** When adding fractions with different denominators, always find the least common denominator (LCD) to make calculations easier!

Learn how to simplify the complex fraction \frac{1}{3 + \frac{1}{4}} by first adding fractions with different denominators and then using the reciprocal rule for division. This step-by-step guide is perfect for students in Grades 6-8.

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