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The given expression appears to be:

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

### Steps to simplify:

1. Let \( y = x + 3 \), so the expression becomes:
   \[
   \frac{3 - \frac{1}{y}}{3 + \frac{1}{y}}
   \]

2. Multiply both the numerator and the denominator by \( y \) to eliminate the fractions inside the larger fraction:
   \[
   \frac{y(3 - \frac{1}{y})}{y(3 + \frac{1}{y})} = \frac{y \cdot 3 - 1}{y \cdot 3 + 1}
   \]

3. Simplify the expression:
   \[
   \frac{3y - 1}{3y + 1}
   \]

4. Substitute \( y = x + 3 \) back:
   \[
   \frac{3(x + 3) - 1}{3(x + 3) + 1} = \frac{3x + 9 - 1}{3x + 9 + 1} = \frac{3x + 8}{3x + 10}
   \]

5. Factor out a common factor of 2 from the denominator (if needed for further simplification):
   \[
   \frac{3x + 8}{2(3x + 5)}
   \]

Thus, the simplified form of the given expression is:

\[
\frac{3x + 8}{3x + 10}
\]

Would you like further details, or do you have any questions?

### Related questions:
1. How do you simplify fractions with variables in both the numerator and the denominator?
2. How can you handle complex rational expressions more easily?
3. What are other ways to factor polynomial expressions?
4. Can you explain how to perform polynomial long division?
5. What is the importance of factoring in simplifying expressions?

### Tip:
Always multiply through by the least common denominator (LCD) to eliminate fractions within a fraction for easier simplification.

Simplify the expression: \frac{3 - \frac{1}{x+3}}{3 + \frac{1}{x+3}}

Simplify the complex rational expression \frac{3 - \frac{1}{x+3}}{3 + \frac{1}{x+3}} using algebraic techniques. Learn how to simplify fractions and expressions with variables, suitable for students in Grades 10-12.

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