**Which of the following rational expressions has the domain restrictions x equals short dash 6 and x equals 1?**

To determine which rational expression has the domain restrictions \( x = -6 \) and \( x = 1 \), we need to understand that domain restrictions in rational expressions occur where the denominator is equal to zero. So, let's look for a denominator that would be zero at \( x = -6 \) and \( x = 1 \).

### Process:
1. **Set up the denominator**: The restrictions occur where the denominator is zero, so the denominator should factor to something like \( (x + 6)(x - 1) \).

2. **Form the rational expression**: The rational expression could be any function that has this denominator. For example:
   \[
   \frac{\text{some numerator}}{(x + 6)(x - 1)}
   \]

### Example Rational Expressions:
- \(\frac{1}{(x + 6)(x - 1)}\)
- \(\frac{x}{(x + 6)(x - 1)}\)
- \(\frac{x^2 + 2}{(x + 6)(x - 1)}\)

All of these expressions will have domain restrictions at \( x = -6 \) and \( x = 1 \), because the denominator becomes zero at those values of \( x \).

So, any rational expression of the form:
\[
\frac{\text{numerator}}{(x + 6)(x - 1)}
\]
would have the domain restrictions \( x = -6 \) and \( x = 1 \).

Do you want more details or have any questions?

---

Here are five related questions:
1. How do you find the domain of a rational expression?
2. What happens if a value makes both the numerator and denominator zero?
3. Can a rational expression have more than two domain restrictions?
4. How do you simplify a rational expression with complex domain restrictions?
5. What are the implications of domain restrictions in real-world problems?

**Tip:** Always factor the denominator of a rational expression completely to easily identify the domain restrictions.

Explore how to determine domain restrictions in rational expressions with a detailed explanation. This problem discusses factors affecting domain, including how to identify where the denominator becomes zero. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation