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The question asks which of the provided expressions is equivalent to \( \frac{1}{3} \).

Let's go through the options one by one to simplify each and compare with \( \frac{1}{3} \).

### Option 1:
\[
\frac{3d}{3d+1} + \frac{1}{3d+1}
\]
The common denominator is \( 3d + 1 \), so:
\[
\frac{3d + 1}{3d+1} = 1
\]
Thus, the simplified result is 1, which is not equal to \( \frac{1}{3} \).

### Option 2:
\[
\frac{d+5}{3d+3} - \frac{4}{3d+3}
\]
The common denominator is \( 3d + 3 \), so:
\[
\frac{(d+5) - 4}{3d+3} = \frac{d+1}{3(d+1)} = \frac{1}{3}
\]
Thus, this expression simplifies to \( \frac{1}{3} \), which matches.

### Option 3:
\[
\frac{2}{3d} - \frac{1}{3d}
\]
Simplifying this gives:
\[
\frac{2 - 1}{3d} = \frac{1}{3d}
\]
This is not equal to \( \frac{1}{3} \).

### Option 4:
\[
\frac{d}{d+3} + \frac{1}{d+3}
\]
The common denominator is \( d + 3 \), so:
\[
\frac{d + 1}{d+3}
\]
This does not simplify to \( \frac{1}{3} \).

### Conclusion:
The correct answer is **Option 2**, which simplifies to \( \frac{1}{3} \).

Would you like further details on any step?

Here are 5 related questions for further practice:
1. How would you simplify \( \frac{2d+4}{2d+6} \)?
2. How can you verify that an expression is equivalent to a given fraction?
3. What are the steps to finding a common denominator in rational expressions?
4. How would you factor the expression \( 3d + 3 \)?
5. How do you handle subtraction of fractions with a common denominator?

**Tip:** When simplifying expressions, always check for common factors to see if they can be reduced.

Learn how to determine which rational expression is equivalent to 1/3 by simplifying fractions. This algebra problem covers key concepts of adding and subtracting rational expressions and simplifying fractions. Suitable for students in Grades 9-11.

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