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.