The expression you provided is:

\[
\frac{2ab}{ab + 3a^2}
\]

To simplify this expression, let's check for common factors in both the numerator and the denominator.

### Step-by-step simplification:
1. **Numerator**: The numerator is \( 2ab \).
2. **Denominator**: The denominator is \( ab + 3a^2 \).

Since both terms in the denominator share a common factor of \( a \), we can factor out \( a \):

\[
ab + 3a^2 = a(b + 3a)
\]

Now the expression becomes:

\[
\frac{2ab}{a(b + 3a)}
\]

3. **Simplify**: Since \( a \) is a common factor in both the numerator and the denominator, you can cancel out \( a \) (assuming \( a \neq 0 \)):

\[
\frac{2ab}{a(b + 3a)} = \frac{2b}{b + 3a}
\]

This is the simplified form of the expression.

### Final Answer:
\[
\frac{2b}{b + 3a}
\]

Do you want further details or have any other questions?

Here are 5 related questions you might find interesting:
1. How do you handle expressions where both numerator and denominator have common factors?
2. How would you simplify expressions that involve higher powers of variables?
3. Can you cancel terms in a fraction if they are added instead of multiplied?
4. How does factoring help in simplifying complex algebraic expressions?
5. What happens if one of the variables equals zero in such expressions?

**Tip**: Always check for common factors in the numerator and denominator before attempting to cancel terms. This simplifies the process and reduces errors.

Simplify the expression \frac{2ab}{ab + 3a^2}.

Learn how to simplify the algebraic fraction \frac{2ab}{ab + 3a^2} by factoring common terms and reducing the expression step-by-step. This guide covers key algebraic concepts such as factoring and simplification, suitable for students in Grades 8-10.

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