1/6(9x + 15). Make it a rational expression a common denominator

To rewrite the expression \(\frac{1}{6}(9x + 15)\) as a rational expression with a common denominator, let's first expand and express it as a single fraction.

Start by distributing \(\frac{1}{6}\) across the expression inside the parentheses:

\[
\frac{1}{6}(9x + 15) = \frac{1}{6} \times 9x + \frac{1}{6} \times 15 = \frac{9x}{6} + \frac{15}{6}
\]

Now, simplify each term:

\[
\frac{9x}{6} = \frac{3x}{2}
\]
\[
\frac{15}{6} = \frac{5}{2}
\]

So the expression becomes:

\[
\frac{3x}{2} + \frac{5}{2}
\]

Since both terms now have a common denominator (2), we can combine them into a single fraction:

\[
\frac{3x + 5}{2}
\]

Thus, the rational expression with a common denominator is \(\frac{3x + 5}{2}\).

Would you like more details, or do you have any questions?

Here are five related questions:
1. How can you combine fractions with different denominators?
2. What are some ways to simplify algebraic expressions?
3. How do you factor algebraic expressions to simplify them?
4. Can you explain how to find the least common denominator for more complex fractions?
5. What is the significance of rewriting expressions with a common denominator in algebra?

**Tip:** When combining fractions, always ensure that the denominators are the same before adding or subtracting the numerators.

Learn how to rewrite the expression 1/6(9x + 15) as a rational expression with a common denominator. This problem covers rational expressions and the process of combining fractions with different denominators. Suitable for students in Grades 7-9.

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