Let's simplify the expression [tex]\(\frac{2 a b}{6 a}\)[/tex] step by step.
### Step 1: Factorize the terms
We begin by separating the constants, variables, and coefficients in both the numerator and the denominator.
- Numerator: [tex]\(2ab\)[/tex]
- Denominator: [tex]\(6a\)[/tex]
### Step 2: Cancel the common factors
In both the numerator and the denominator, we have the factor [tex]\(a\)[/tex].
[tex]\[
\frac{2ab}{6a} = \frac{2b}{6}
\][/tex]
### Step 3: Simplify the fraction further
Now, we simplify the fraction [tex]\(\frac{2b}{6}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 2 and 6 is 2.
[tex]\[
\frac{2b}{6} = \frac{2b \div 2}{6 \div 2} = \frac{b}{3}
\][/tex]
### Conclusion
The simplified form of the expression [tex]\(\frac{2ab}{6a}\)[/tex] is:
[tex]\[
\boxed{\frac{b}{3}}
\][/tex]
