Problem 2

Question

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

Step-by-Step Solution

Verified
Answer
The number -9 needs to be excluded from the domain of the given rational expression.
1Step 1: Identify the Denominator
The denominator of the given rational expression is \(x+9\). This part of the expression cannot be equal to zero, because division by zero would make the expression undefined.
2Step 2: Set the Denominator Equal to Zero
Set the denominator \(x+9\) equal to zero. The equation to solve is \(x + 9 = 0\).
3Step 3: Solve for x
Solve the equation for x by subtracting 9 from both sides, which gives \(x = -9\).
4Step 4: Identify the Excluded Number
The solution of the equation is the number that must be excluded from the domain of the rational expression.