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The equation you have provided is:

\[
y = \frac{3x + 1}{2x + 6}
\]

Would you like to solve this equation for a specific value of \( x \), or are you looking for an analysis such as finding the asymptotes, intercepts, or another form of simplification? Let me know what you'd like to explore further.

Here are some next steps we can take:

1. Solve for \( x \) when \( y \) is given.
2. Find the x-intercept(s) and y-intercept of this equation.
3. Simplify the expression if possible.
4. Determine vertical and horizontal asymptotes.
5. Analyze the behavior of the function as \( x \to \infty \) or \( x \to -\infty \).

**Tip:** When dealing with rational functions like this one, vertical asymptotes occur when the denominator equals zero (if it doesn't cancel out with the numerator).

Explore the rational function y = (3x + 1) / (2x + 6) by simplifying, solving for specific values, and determining asymptotes. This algebraic problem is suitable for students in Grades 9-12 and covers key concepts like vertical and horizontal asymptotes.

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