/*! 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 8 Simplify each rational expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 8

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{4 x-8}{x^{2}-4 x+4}$$

Short Answer

Expert verified
The simplified expression is \(\frac{4}{x - 2}\) and the number that must be excluded from the domain is \(2\).

Step by step solution

01

Factor the Expression

Firstly, factor both the numerator and the denominator. The numerator \(4x - 8\) can be factored by taking out the common factor of \(4\), which leaves us with \(4(x - 2)\). The denominator is a quadratic which factors to \((x - 2)^{2}\).
02

Simplify the Expression

Now that both the numerator and the denominator are factored, cancel out the same factors from the numerator and the denominator. The term \((x - 2)\) appears in both the numerator and denominator, hence we can cancel it out. This simplifies our expression to \(\frac{4}{x - 2}\).
03

Identify the Excluded Values

A number must be excluded from the domain if it makes the denominator of the simplified expression equal to zero, as division by zero is undefined. Setting \(x - 2 = 0\) and solving for \(x\), we get \(x = 2\). So, \(2\) must 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 factor the difference of two squares. Provide an example with your explanation.

Explain how to factor \(3 x^{2}+10 x+8\)

Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime of 80 years. Round the decimal factor in your scientific notation answer to two decimal places.

Simplify using properties of exponents. $$\left(3 x^{\frac{2}{3}}\right)\left(4 x^{\frac{3}{4}}\right)$$

Simplify using properties of exponents. $$\frac{\left(2 y^{\frac{1}{5}}\right)^{4}}{y^{\frac{3}{10}}}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete 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.