To simplify the given algebraic expression [tex]\(\frac{12xy}{3y}\)[/tex], follow these step-by-step instructions:
1. Identify common factors in the numerator and the denominator:
- The numerator is [tex]\(12xy\)[/tex].
- The denominator is [tex]\(3y\)[/tex].
2. Factor out the common term in both the numerator and the denominator:
- Notice that both the numerator and the denominator have a [tex]\( y \)[/tex] term.
3. Simplify by canceling out the common term:
- When you cancel out the [tex]\( y \)[/tex] term from both the numerator and the denominator, you get:
[tex]\[
\frac{12xy}{3y} = \frac{(12x \cdot y)}{(3 \cdot y)} = \frac{12x}{3}
\][/tex]
4. Simplify the remaining expression:
- The remaining expression is [tex]\(\frac{12x}{3}\)[/tex].
- Divide [tex]\(12x\)[/tex] by [tex]\(3\)[/tex]:
[tex]\[
\frac{12x}{3} = 4x
\][/tex]
So, the simplified form of the given expression [tex]\(\frac{12xy}{3y}\)[/tex] is:
[tex]\[
4x
\][/tex]
