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The expression provided is:

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

Let's simplify this step by step:

### Step 1: Simplify the denominator
The denominator is \(\frac{3}{x} + \frac{1}{x}\). Since both terms have the same denominator, we can add them together:

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

### Step 2: Simplify the entire expression
Now, substitute the simplified denominator back into the original expression:

\[
\frac{x}{\frac{4}{x}}
\]

When dividing by a fraction, we multiply by its reciprocal. So:

\[
\frac{x}{\frac{4}{x}} = x \cdot \frac{x}{4} = \frac{x^2}{4}
\]

### Final Answer:
The simplified expression is:

\[
\frac{x^2}{4}
\]

Would you like more details, or do you have any questions about this process?

Here are 5 related questions you might explore:
1. How can I simplify more complex algebraic fractions?
2. What are the properties of exponents when simplifying expressions?
3. How can the concept of reciprocals help in division of fractions?
4. How do you add fractions with different denominators?
5. How does the structure of a rational function affect its graph?

**Tip:** Always look for common denominators when adding or subtracting fractions!

Simplify the algebraic expression x / (3/x + 1/x)

Learn how to simplify the algebraic expression x / (3/x + 1/x) with a step-by-step solution. This problem covers key algebraic concepts, including the simplification of fractions, reciprocals, and the addition of fractions with a common denominator. Suitable for students in Grades 7-9.

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