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Chapter 0: Problem 98

Explain how to determine which numbers must be excluded from the domain of a rational expression.

Short Answer

Expert verified
The numbers which are the solutions to the equation where the denominator of the rational expression is set to zero must be excluded from the domain of the function as they would make the fraction undefined.

Step by step solution

01

Identify the Rational Function

The initial step in this process is to identify the given rational function or expression. A rational function can typically be written in the form \(f(x) = \frac{P(x)}{Q(x)}\) where \(P(x)\) and \(Q(x)\) are polynomial functions.
02

Identify the Denominator

The next step is to consider the denominator of the function \(Q(x)\). This is important because the denominator of the function is what we are concerned about. It should never be equal to zero as this causes the function to be undefined.
03

Set Denominator to Zero

The third step is to set the denominator equal to zero and solve for \(x\). It means that we will find the values of \(x\) for which the denominator becomes zero.
04

Excluded Numbers for Domain

Lastly, take note of these values because they are the numbers we must exclude from the domain of the rational expression. These values make the denominator zero and result in an undefined operation in mathematics.

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Most popular questions from this chapter

The average rate on a round-trip commute having a one-way distance \(d\) is given by the complex rational expression $$\frac{2 d}{\frac{d}{r_{1}}+\frac{d}{r_{2}}}$$ in which \(r_{1}\) and \(r_{2}\) are the average rates on the outgoing and return trips, respectively. Simplify the expression. Then find your average rate if you drive to campus averaging 40 miles per hour and return home on the same route averaging 30 miles per hour. Explain why the answer is not 35 miles per hour.

Perform the indicated operations. Simplify the result, if possible. $$\left(4-\frac{3}{x+2}\right)\left(1+\frac{5}{x-1}\right)$$

Explain how to determine the restrictions on the variable for the equation $$ \frac{3}{x+5}+\frac{4}{x-2}=\frac{7}{x^{2}+3 x-6} $$

If you are given a quadratic equation, how do you determine which method to use to solve it?

Will help you prepare for the material covered in the next section. A telephone texting plan has a monthly fee of \(\$ 20\) with a charge of \(\$ 0.05\) per text. Write an algebraic expression that models the plan's monthly cost for \(x\) text messages.
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