Problem 87
Question
Explain how to determine which numbers must be excluded from the domain of a rational expression.
Step-by-Step Solution
Verified Answer
The numbers that must be excluded from the domain of a rational expression are those values for the variable that would make the denominator equal to zero.
1Step 1: Identify the Denominator
Determine the denominator of the rational expression. This is the bottom part of the fraction.
2Step 2: Set the Denominator Equal to Zero
Write out an equation that sets the denominator of the rational expression equal to zero.
3Step 3: Solve for the Variable
Solve the equation for the variable. This might involve factoring the denominator or using the quadratic equation, depending on how complex the denominator is.
4Step 4: Exclude the Values
The solution(s) to the equation are the values that must be excluded from the domain of the rational expression. In other words, these are the values of the variable that will make the denominator equal to zero and, therefore, the entire rational expression undefined.
Other exercises in this chapter
Problem 87
Factor completely, or state that the polynomial is prime. $$ 9 b^{2} x-16 y-16 x+9 b^{2} y $$
View solution Problem 87
Perform the indicated operation or operations. $$ (2 x+5)(2 x-5)\left(4 x^{2}+25\right) $$
View solution Problem 87
In Exercises 87–106, perform the indicated computations. Write the answers in scientifi c notation. If necessary, round the decimal factor in your scientifi c n
View solution Problem 87
Simplify algebraic expression. \(5(3 x-2)+12 x\)
View solution