Sure, I'd be happy to help you with that!
To reduce the given fraction [tex]\(\frac{3x}{6x^2}\)[/tex] to its lowest terms, we should follow these steps:
1. Write down the fraction:
[tex]\[
\frac{3x}{6x^2}
\][/tex]
2. Factor the numerator and the denominator:
[tex]\[
\frac{3x}{6x^2} = \frac{3x}{6 \cdot x \cdot x}
\][/tex]
3. Cancel out the common factors in the numerator and the denominator:
- Both the numerator and the denominator have the common factor [tex]\(3x\)[/tex].
- So we can divide both the numerator and the denominator by [tex]\(3x\)[/tex].
[tex]\[
\frac{3x}{6x^2} = \frac{3x \div 3x}{6x^2 \div 3x} = \frac{1}{2x}
\][/tex]
4. Simplified form:
After canceling out the common factor, we are left with:
[tex]\[
\frac{1}{2x}
\][/tex]
Therefore, the fraction [tex]\(\frac{3x}{6x^2}\)[/tex] simplifies to [tex]\(\frac{1}{2x}\)[/tex].
