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To solve the problem, we need to multiply the two rational expressions given:

\[
\frac{x-3}{x+5} \times \frac{3x}{x-5}
\]

Multiplying these two fractions, we get:

\[
\frac{(x-3) \times 3x}{(x+5) \times (x-5)}
\]

Simplifying the numerator and the denominator:

\[
\frac{3x(x-3)}{(x+5)(x-5)}
\]

Expanding the expressions:

\[
\frac{3x^2 - 9x}{x^2 - 25}
\]

Therefore, the correct product of the given rational expressions is \( \frac{3x^2 - 9x}{x^2 - 25} \), which corresponds to option B:

\[
B. \frac{3x^2 - 9x}{x^2 - 25}
\]

Do you have any more questions or need further details on this problem?

### Related Questions
1. What happens to the expression if \( x = 5 \) or \( x = -5 \)?
2. Can you simplify the expression \( \frac{3x^2 - 9x}{x^2 - 25} \) further?
3. How would you factorize the denominator \( x^2 - 25 \)?
4. What is the domain of the rational expression \( \frac{3x^2 - 9x}{x^2 - 25} \)?
5. How does the location of zeros in the numerator affect the graph of the rational function?

### Tip
Always check the domain of a rational expression to avoid undefined values, which occur where the denominator equals zero.

Which of the following is the product of the rational expressions shown below? (x-3)/(x+5) * (3x)/(x-5)

Learn how to multiply rational expressions such as (x-3)/(x+5) and (3x)/(x-5) in this step-by-step solution. This problem explores algebraic concepts including simplifying fractions and factoring. Suitable for students in Grades 8-10.

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