5x-15                 x3
--------    x    ---------
4x2                 6x-18

The given expression can be simplified by multiplying the two fractions. Here's how we simplify step by step:

### Expression:

\[
\frac{5x - 15}{4x^2} \times \frac{x^3}{6x - 18}
\]

### Step 1: Factorize each term

1. **Factorize \( 5x - 15 \):**

   \[
   5x - 15 = 5(x - 3)
   \]

2. **Factorize \( 6x - 18 \):**

   \[
   6x - 18 = 6(x - 3)
   \]

### Step 2: Rewrite the expression with factored terms

\[
\frac{5(x - 3)}{4x^2} \times \frac{x^3}{6(x - 3)}
\]

### Step 3: Simplify by canceling common factors

- Cancel \((x - 3)\) from the numerator and denominator:

\[
\frac{5}{4x^2} \times \frac{x^3}{6}
\]

- Now multiply the fractions:

\[
\frac{5 \cdot x^3}{4x^2 \cdot 6} = \frac{5x^3}{24x^2}
\]

### Step 4: Simplify further by canceling \(x^2\):

\[
\frac{5x^{3-2}}{24} = \frac{5x}{24}
\]

### Final Simplified Expression:

\[
\frac{5x}{24}
\]

Would you like further clarification or have any questions about the steps?

### Related Questions:

1. How do you simplify complex rational expressions involving multiple factors?
2. What is the process of factoring polynomials like \(5x - 15\) and \(6x - 18\)?
3. How do you multiply and simplify algebraic fractions step-by-step?
4. How can you identify and cancel common factors in algebraic fractions?
5. What are the rules for simplifying expressions with exponents during multiplication?

**Tip:** Always factorize expressions first before multiplying or dividing fractions; it helps to cancel out terms easily.

Explore the step-by-step process of simplifying algebraic expressions, including factoring and multiplying fractions. Learn key concepts like factorization and simplification, suitable for students in Grades 9-10.

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