QuestionFind the domain of $x$ in the expression $\frac{x}{x+79}$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $\frac{x}{x+79}$ . . We are looking for the domain of the variable $x$ .
3. The domain of a function or expression is the set of all possible values of the variable that make the expression defined.

STEP 2

In the given expression, the denominator is $x+79$ . For any rational expression, the denominator cannot be equal to zero because division by zero is undefined.
So, we set the denominator equal to zero and solve for $x$ .
$x+79 =0$

STEP 3

Subtract79 from both sides of the equation to isolate $x$ .
$x = -79$

STEP 4

This means that the expression is undefined when $x = -79$ . Therefore, the domain of the expression is all real numbers except $-79$ .
We can write this in interval notation as $(-\infty, -79) \cup (-79, \infty)$ .
So, the domain of the variable $x$ in the given expression is $(-\infty, -79) \cup (-79, \infty)$ .

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