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The given expression is:

\[
\frac{3t + 6t^2}{3t}
\]

### Step-by-Step Simplification:

1. **Factor the numerator**: 
   Both terms in the numerator \(3t + 6t^2\) have a common factor of \(3t\). So, factor out \(3t\):
   \[
   3t + 6t^2 = 3t(1 + 2t)
   \]

2. **Rewrite the expression**:
   \[
   \frac{3t(1 + 2t)}{3t}
   \]

3. **Cancel the common factor**:
   The \(3t\) in the numerator and denominator cancel out:
   \[
   1 + 2t
   \]

### Final Answer:
\[
1 + 2t
\]

Would you like more details or have any other questions?

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Here are 5 related questions:
1. How do you factor expressions with higher-degree terms?
2. What is the importance of canceling common terms in fractions?
3. How do you handle expressions that involve variables in both the numerator and denominator?
4. Can you always cancel out terms that appear in both the numerator and denominator?
5. How would you simplify an expression if there were multiple variables?

**Tip**: Always check for common factors before performing any other operations. This makes simplification much easier!

Simplify by factoring and canceling: (3t + 6t^2) / 3t

This page provides a step-by-step simplification of the rational expression (3t + 6t^2) / 3t by factoring and canceling common terms. Learn how to apply factoring and the distributive property to simplify algebraic fractions. Suitable for students in Grades 7-9.

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