https://file.aiquickdraw.com/mathbot/file/17273694713263s6jol0w.jpg

The task is to identify the permissible values of the variable \( x \) in the expression \(\frac{x^2 - 1}{6}\).

### Step-by-step Analysis:
The expression provided is \(\frac{x^2 - 1}{6}\).

1. **Domain Analysis**: 
   - Since the denominator is a constant (6), it is never zero. Therefore, there are no restrictions imposed by the denominator.
   - The numerator \(x^2 - 1\) has no impact on the domain since there are no divisions by \(x\), square roots, or logarithms that would limit the values of \(x\).

2. **Conclusion**:
   The expression is defined for all real numbers, meaning there are no restrictions on \(x\).

### Correct Answer:
The correct option chosen in the image is "all numbers except -1," which is incorrect. The accurate answer should be "all numbers," indicating that \(x\) can take any real value.

Would you like more details or have any questions?

### Related Questions:
1. What is the domain of a rational expression in general?
2. How does the value of the denominator affect the domain of an expression?
3. Why is it important to consider both numerator and denominator in rational expressions?
4. How would the expression change if the denominator contained a variable?
5. What happens if the numerator of a fraction becomes zero?

**Tip:** Always check both numerator and denominator when determining the domain of a rational expression.

Укажите допустимые значения переменной x в выражении (x^2 - 1)/6.

Discover how to determine the domain of the rational expression (x^2 - 1)/6, focusing on the key algebraic principles and rational expression rules. Suitable for Grades 8-10.

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