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The expression in question is \(\frac{x + 8}{7x + 6}\).

To determine the domain of a rational expression, we need to find where the denominator is zero because division by zero is undefined. Therefore, we set the denominator equal to zero and solve for \(x\):

\[
7x + 6 = 0
\]

Solve for \(x\):

\[
7x = -6 \quad \Rightarrow \quad x = -\frac{6}{7}
\]

Thus, the expression is undefined when \(x = -\frac{6}{7}\). The domain of the expression is all real numbers except \(x = -\frac{6}{7}\).

From the options, the correct answer is:

**All real numbers \(x\) such that \(x \neq -\frac{6}{7}\).**

Would you like a detailed explanation of any step?

Here are 5 questions related to domain and rational expressions:
1. How do you find the domain of a rational function in general?
2. What happens when the denominator of a rational function equals zero?
3. How does factoring the denominator help in finding domain restrictions?
4. Can a rational function have a domain that includes only positive real numbers?
5. How do you determine the vertical asymptotes of a rational function?

**Tip:** Always check for domain restrictions by setting the denominator equal to zero when working with rational expressions.

Find the domain of the expression: (x + 8) / (7x + 6).

Learn how to find the domain of a rational expression such as (x + 8) / (7x + 6). This problem teaches key algebraic concepts, including how to determine where a function is undefined due to division by zero. Suitable for high school students.

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