Problem 2 - College Algebra

Question

Find all numbers that must be excluded from the domain of each rational expression. $$\frac{13}{x+9}$$

Step-by-Step Solution

Answer

The number -9 must be excluded from the domain of the given rational expression.

Step 1: Set the Denominator Equal to Zero

The first step is to set the denominator of the rational function equal to zero. So, let's set \(x + 9 = 0\).

Step 2: Solve for x

For solving the equation \(x + 9 = 0\), we should subtract 9 from both sides of the equation. This will result in \(x = -9\)

Step 3: Interpret the Result

The solution, \(x = -9\), is the number that would make the denominator of the rational function 0. So, it must be excluded from the domain of the rational function.