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To solve for the area of the toilet/bathroom, we need to multiply the length and width expressions provided.

The length is given as:

\[
\frac{x - 3}{x^2 + 5x - 24}
\]

The width is given as:

\[
\frac{x + 8}{x^2 + 5x - 24}
\]

### Step 1: Multiply the length and width expressions
To find the area, multiply these two fractions:

\[
\left( \frac{x - 3}{x^2 + 5x - 24} \right) \times \left( \frac{x + 8}{x^2 + 5x - 24} \right)
\]

\[
= \frac{(x - 3)(x + 8)}{(x^2 + 5x - 24)^2}
\]

### Step 2: Factor the denominator

We need to factor \(x^2 + 5x - 24\). This can be factored into:

\[
x^2 + 5x - 24 = (x - 3)(x + 8)
\]

### Step 3: Simplify the expression

Now, substitute the factored form of the denominator into the area formula:

\[
= \frac{(x - 3)(x + 8)}{((x - 3)(x + 8))^2}
\]

Cancel out one factor of \((x - 3)(x + 8)\) from the numerator and denominator:

\[
= \frac{1}{(x - 3)(x + 8)}
\]

### Final Answer

The area of the toilet/bathroom is:

\[
\frac{1}{(x - 3)(x + 8)}
\]

---

Would you like to discuss any of the steps in detail or need further clarifications?

Here are 5 related questions for further practice:

1. What happens to the area as \(x\) approaches 3 or -8?
2. Can you find the area if \(x = 2\)?
3. How would the expression change if the dimensions were swapped (i.e., if width was \(\frac{x-3}{x^2 + 5x - 24}\) and length was \(\frac{x+8}{x^2 + 5x - 24}\))?
4. What type of function represents the area in terms of \(x\)?
5. How does factoring help simplify rational expressions?

**Tip:** Always factor both the numerator and denominator of a rational expression before attempting to simplify—it often reveals cancellations that can make the problem easier.

Solve for the area of a toilet/bathroom where the length is (x - 3) / (x^2 + 5x - 24) and the width is (x + 8) / (x^2 + 5x - 24).

Learn how to solve for the area of a toilet/bathroom by multiplying rational expressions. This algebra problem covers factoring quadratics and simplifying rational expressions. Suitable for students in Grades 9-11.

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