https://file.aiquickdraw.com/mathbot/file/1725529570692d4p38r9n.jpg

The expression given is:

\[
\frac{3x(2x + 3y)}{15z} \div \frac{3x}{5z}
\]

We need to simplify this expression step by step:

### Step 1: Convert division into multiplication
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, rewrite the division as:

\[
\frac{3x(2x + 3y)}{15z} \times \frac{5z}{3x}
\]

### Step 2: Cancel common factors
Now, we can cancel out terms that are common in both the numerator and denominator:
- \(3x\) in the numerator of the first fraction and the denominator of the second fraction cancel each other out.
- \(z\) in the denominator of the first fraction and the numerator of the second fraction also cancel each other out.

After canceling, we are left with:

\[
\frac{(2x + 3y)}{3}
\]

### Final Simplified Expression:

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

Thus, the correct simplification is \(\frac{2x + 3y}{3}\).

Would you like more details or further explanation on any part of this solution? 

Here are 5 related questions:
1. How do you multiply and divide fractions?
2. What are the steps to factor polynomials in fraction simplification?
3. Can you explain how to cancel out terms in more complex algebraic expressions?
4. How do you simplify algebraic expressions with multiple variables?
5. How would the expression change if we introduced exponents?

**Tip:** Always cancel common factors between numerators and denominators before performing further calculations.

Which is the correct simplification of: \( \frac{3x(2x + 3y)}{15z} \div \frac{3x}{5z} \)?

Learn how to simplify the algebraic expression \( \frac{3x(2x + 3y)}{15z} \div \frac{3x}{5z} \) step by step. This problem covers fraction division and simplification of algebraic terms. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation