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Chapter 0: Problem 4

Find all numbers that must be excluded from the domain of each rational expression. $$\frac{x+7}{x^{2}-49}$$

Short Answer

Expert verified
The numbers that must be excluded from the domain of the given rational expression are \(x = 7\) and \(x = -7\).

Step by step solution

01

Identify the denominator

The denominator of the rational expression is \(x^2 - 49\).
02

Set the denominator equal to zero

In order to find which x-values to exclude, we need to find what x-values can make the denominator zero. So you set \(x^2 - 49 = 0\).
03

Solve the equation

Solve the equation for \(x\). This equation is a difference of squares, which can be factored as \((x - 7)(x + 7) = 0\). Setting these equal to zero gives us \(x = 7\) and \(x = -7\).
04

Conclude the result

The solutions of the equation are the x-values we need to exclude from the domain. Hence, \(x = 7\) and \(x = -7\) must be excluded from the domain.

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Most popular questions from this chapter

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. The toll to a bridge is \(\$ 3.00 .\) A three-month pass costs \(\$ 7.50\) and reduces the toll to \(\$ 0.50 .\) A six-month pass costs \(\$ 30\) and permits crossing the bridge for no additional fee. How many crossings per three-month period does it take for the three-month pass to be the best deal?

How is the quadratic formula derived?

$$\text { Solve for } t: \quad s=-16 t^{2}+v_{0} t$$

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

What is a rational expression?
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