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.