/*! 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 7 Find all numbers for which each ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 7

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{x+3}{(x+9)(x-2)}$$

Short Answer

Expert verified
The expression \(\frac{x+3}{(x+9)(x-2)}\) is undefined for \(x = -9\) and \(x = 2\).

Step by step solution

01

Set the factors in the denominator equal to zero

To find for which values the expression is undefined, we set each factor of the denominator equal to zero and solve for \(x\). This means we have the equations \(x + 9 = 0\) and \(x - 2 = 0\).
02

Solve the equations

By solving the equation \(x + 9 = 0\), we get \(x = -9\). Similarly, after solving \(x - 2 = 0\), we have \(x = 2\).
03

Present the undefined values

The rational expression \(\frac{x+3}{(x+9)(x-2)}\) is undefined for the values \(x = -9\) and \(x = 2\), as these make the denominator equal to zero, which in turn makes the entire expression undefined.

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

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6}{x-1}-\frac{5}{1-x}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{3-x}{x-7}-\frac{2 x-5}{7-x}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-3}+\frac{9}{3-x}$$

Solve: \(x^{2}-12 x+36=0 .\) (Section 6.6, Example 4)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4-x}{x-9}-\frac{3 x-8}{9-x}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.