The question in the image involves subtracting two rational expressions and simplifying the result.

We are tasked with subtracting:

$\frac{x^2}{x^2 - 5x - 36} - \frac{36}{x^2 - 5x - 36}$

Step-by-step:

1. Factor the denominator: Both fractions have the same denominator, $x^2 - 5x - 36$, so we can simply combine the numerators.

   The denominator factors as: $x^2 - 5x - 36 = (x + 4)(x - 9)$

2. Combine the numerators: Since the denominators are the same, subtract the numerators: $\frac{x^2 - 36}{(x + 4)(x - 9)}$

3. Factor the numerator: The numerator $x^2 - 36$ is a difference of squares, so it factors as: $x^2 - 36 = (x + 6)(x - 6)$

4. Final expression: Now the rational expression becomes: $\frac{(x + 6)(x - 6)}{(x + 4)(x - 9)}$

This is the simplified form of the difference.

Answer Choice: The correct answer is $(x + 6)(x - 6) / (x + 4)(x - 9)$, which matches one of the provided options.

Would you like more details or further explanation? Here are some related questions for practice:

1. How do you factor a quadratic trinomial?
2. What is the difference of squares formula?
3. How can you simplify expressions with common denominators?
4. What happens when you subtract rational expressions with different denominators?
5. How do you find the domain of a rational function?

Tip: Always ensure the denominators are factored fully before simplifying expressions.