Let's analyze and solve the problem in the image.

The given expression to simplify is:

$\frac{25x^2}{2x + 6} \cdot \frac{2}{5x}.$

In the second step shown in the image, the denominator $2x + 6$ has been factored into $2(x + 3)$, so the expression becomes:

$\frac{25x^2}{2(x + 3)} \cdot \frac{2}{5x}.$

Step-by-step simplification:

1. Factor the numerators and denominators:

   • The expression is: $\frac{25x^2}{2(x + 3)} \cdot \frac{2}{5x}.$
   • Simplify constants and variables separately.

2. Combine the fractions:

   • Multiply the numerators: $25x^2 \cdot 2 = 50x^2.$
   • Multiply the denominators: $2(x + 3) \cdot 5x = 10x(x + 3).$

   The result is: $\frac{50x^2}{10x(x + 3)}.$

3. Simplify the fraction:

   • Cancel $x$ in the numerator and denominator: $\frac{50x^2}{10x(x + 3)} = \frac{50x}{10(x + 3)}.$
   • Simplify $50/10$ to $5$: $\frac{5x}{x + 3}.$

Thus, the simplified product is: $\frac{5x}{x + 3}.$

Final Answer:

The correct choice is 5x/(x + 3).

Would you like more details or have any questions? Here are five related questions to explore further:

1. What are the general steps for simplifying rational expressions involving multiplication?
2. How do you factor polynomials like $2x + 6$?
3. How can you identify and cancel common factors in rational expressions?
4. What are the rules for simplifying expressions with multiple variables?
5. Can you explain why $x + 3$ cannot be canceled unless it's a factor of the numerator?

Tip: Always factor expressions completely before simplifying; it reduces errors and makes the process clearer.