It looks like you’ve uploaded an image of a rational expression involving multiplication. Let me break down the problem for you and simplify it step-by-step.

The expression is:

$\frac{x^2 + 2x - 24}{x^2 - 36} \cdot \frac{x - 6}{x + 5}$

Step 1: Factor the expressions

We will factor the quadratics in the numerator and denominator:

• Numerator of the first fraction: $x^2 + 2x - 24$

  • We need factors of $-24$ that add up to $2$. The numbers $6$ and $-4$ work, so: $x^2 + 2x - 24 = (x + 6)(x - 4)$

• Denominator of the first fraction: $x^2 - 36$

  • This is a difference of squares: $x^2 - 36 = (x + 6)(x - 6)$

Step 2: Substitute the factored expressions into the original equation

Substitute the factored terms into the problem:

$\frac{(x + 6)(x - 4)}{(x + 6)(x - 6)} \cdot \frac{x - 6}{x + 5}$

Step 3: Cancel common factors

Now, we can cancel out the common terms:

• The $(x + 6)$ terms cancel out in the first fraction.
• The $(x - 6)$ terms cancel out between the two fractions.

After canceling, you are left with:

$\frac{x - 4}{x + 5}$

Final Answer:

$\frac{x - 4}{x + 5}$

This is the simplified expression.

Would you like further details on any step of the process? Let me know if you have any more questions!

Here are 5 follow-up questions for you:

1. How do you factor a quadratic expression?
2. Can you explain the difference of squares formula?
3. What happens if there are no common factors to cancel out in rational expressions?
4. How would you handle a division problem between polynomials instead of multiplication?
5. What are the restrictions on the variable in this problem?

Tip: Always look for common factors before canceling terms in a rational expression to make the simplification process easier.