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.
Other exercises in this chapter
Problem 2
Evaluate each algebraic expression for the given value or values of the variable(s). $$8+6 x, \text { for } x=5$$
View solution Problem 2
Evaluate each exponential expression. $$6^{2} \cdot 2$$
View solution Problem 2
$$\text { Factor out the greatest common factor.}$$ $$16 x-24$$
View solution Problem 2
Evaluate each expression in Exercises \(1-12,\) or indicate that the root is not a real number. $$\sqrt{25}$$
View solution