The problem asks to find the domain of the expression $\frac{x}{x+7}$. The domain is the set of all possible values of $x$ for which the expression is defined.

1. Problem Description

The problem asks to find the domain of the expression $\frac{x}{x+7}$. The domain is the set of all possible values of $x$ for which the expression is defined.

2. Solution Steps

The expression $\frac{x}{x+7}$ is a rational expression. A rational expression is undefined when the denominator is equal to zero. Therefore, we need to find the values of $x$ for which $x+7 = 0$.

$x + 7 = 0$

$x = -7$

So, the expression is undefined when $x = -7$. Therefore, the domain of the expression is all real numbers except $x = -7$.

In set notation, this is represented as $\{x \mid x \neq -7\}$.

3. Final Answer

{x | x ≠ -7}