/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Find all numbers that must be ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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 -7 and 7.

Step by step solution

01

Setting the denominator equal to zero

Set the denominator equal to zero: \( x^{2}-49 = 0 \).
02

Solve for x

Now, apply the difference of squares to facilitate the solution: \( (x+7)(x-7) = 0 \). Then, the solutions to the equation are given by the roots of each factor: \( x+7=0 \) and \( x-7=0 \). Solving these equations, we find \( x=-7, 7 \).
03

Conclusion for the domain

The numbers -7 and 7 make the denominator equal to zero, thus they should be excluded from the domain of the given rational expression. So, the domain consists of all real numbers except -7 and 7.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ x^{2}+36-(x+6)^{2} $$

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{-\frac{5}{4} y^{\frac{1}{3}}}}{x^{-\frac{3}{4}}}\right)^{-6} $$

Simplify using properties of exponents. $$\frac{72 x^{\frac{3}{4}}}{9 x^{\frac{1}{3}}}$$

Evaluate each expression. $$\sqrt[3]{\sqrt[4]{16}+\sqrt{625}}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.