To simplify the expression [tex]\(\frac{3x + 18}{18}\)[/tex] completely, follow these steps:
1. Factor the numerator where possible.
The numerator is [tex]\(3x + 18\)[/tex]. You can factor out a common factor from both terms. Notice that both terms have a common factor of 3. Therefore, we can write:
[tex]\[
3x + 18 = 3(x + 6)
\][/tex]
2. Rewrite the fraction using the factored form of the numerator.
Substituting [tex]\(3(x + 6)\)[/tex] into the original fraction, we get:
[tex]\[
\frac{3(x + 6)}{18}
\][/tex]
3. Simplify the fraction by canceling common factors.
The denominator is 18, which can be written as [tex]\(3 \times 6\)[/tex]. So, we now have:
[tex]\[
\frac{3(x + 6)}{3 \times 6}
\][/tex]
Since the numerator and the denominator both have a factor of 3, we can cancel this common factor:
[tex]\[
\frac{3(x + 6)}{3 \times 6} = \frac{x + 6}{6}
\][/tex]
4. Express the simplified fraction as a sum of terms if needed.
Finally, we can rewrite [tex]\(\frac{x + 6}{6}\)[/tex] as:
[tex]\[
\frac{x + 6}{6} = \frac{x}{6} + \frac{6}{6} = \frac{x}{6} + 1
\][/tex]
So, the completely simplified form of the expression [tex]\(\frac{3x + 18}{18}\)[/tex] is:
[tex]\[
\frac{x}{6} + 1
\][/tex]
