/*! 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 14 Simplify each rational expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 14

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{x^{2}-14 x+49}{x^{2}-49}$$

Short Answer

Expert verified
\(\frac{x-7}{x+7}\) with \(-7\) excluded from the domain.

Step by step solution

01

Factorization of the Polynomial

Begin by factorizing the numerator and the denominator of the given rational expression. For numerator, \((x^2-14x+49)\) this can be rewritten as \((x-7)^2\). Similarly, for denominator \((x^2-49)\), it can be rewritten as \((x+7)(x-7)\). So, the rational expression becomes: \(\frac{(x-7)^2}{(x+7)(x-7)}\).
02

Simplifying the Rational Expression

Now, cancel out the common factors from the numerator and the denominator. Here, \((x-7)\) is the common factor that can be removed from both the numerator and the denominator. Thus, the simplified form of the given rational expression is \( \frac{x-7}{x+7}\).
03

Identify values that must be excluded from the domain

The denominator of the simplified expression should not be zero as division by zero is undefined. So, draw the equation for the denominator and solve for \(x\). Thus, the equation that will give the values that must be excluded from domain is \(x+7=0\). Simplifying this, \(x=-7\). Hence, \(-7\) should be excluded from the domain.

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 how to multiply rational expressions.

Describe the solution set of \(|x|>-4\)

How is the quadratic formula derived?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.

a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$ \text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. } $$ How old is the son?b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.