The problem in the image presents three expressions to simplify. I'll go through each step for you:

1. Expression 1:

   $\frac{-x^2 + 10x - 24}{48 - 2x - x^2}$

   Let's begin by rewriting the denominator for easier factoring:

   $48 - 2x - x^2 = -x^2 - 2x + 48$

   We factor both the numerator and the denominator.

   Numerator: $-x^2 + 10x - 24$ can be factored as:

   $-(x^2 - 10x + 24) = -(x - 6)(x - 4)$

   Denominator: $-x^2 - 2x + 48$ can be factored as:

   $-(x^2 + 2x - 48) = -(x - 6)(x + 8)$

   Now, the expression becomes:

   $\frac{-(x - 6)(x - 4)}{-(x - 6)(x + 8)}$

   Cancelling out the common factor $(x - 6)$, we get:

   $\frac{x - 4}{x + 8}$

2. Expression 2:

   $\frac{x^2 - 7x + 12}{x^3 + 14x + 48}$

   We need to factor both the numerator and the denominator.

   Numerator: $x^2 - 7x + 12$ factors to:

   $(x - 3)(x - 4)$

   Denominator: $x^3 + 14x + 48$ factors to:

   $(x + 4)(x^2 - 4x + 12)$

   Now, the expression becomes:

   $\frac{(x - 3)(x - 4)}{(x + 4)(x^2 - 4x + 12)}$

   No further simplifications are possible, so this is the simplified form.

Let me know if you'd like further details or explanations on any part of the process!

Here are some related questions to explore:

1. How do you factor quadratic expressions?
2. How do you identify the greatest common factor in polynomials?
3. What are the methods for simplifying rational expressions?
4. Can a cubic polynomial always be factored?
5. What happens when you divide a rational expression by another?

Tip: When simplifying rational expressions, always look for common factors in both the numerator and the denominator to cancel out.