/*! 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 26 Multiply or divide as indicated.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 26

Multiply or divide as indicated. $$\frac{x^{2}-4}{x-2} \div \frac{x+2}{4 x-8}$$

Short Answer

Expert verified
The solution to the operation \(\frac{x^{2}-4}{x-2} \div \frac{x+2}{4x-8}\) is \(\frac{1}{4}x + \frac{1}{2}\).

Step by step solution

01

Simplify the Fractions

Initially, it's important to break down the algebraic expressions. The polynomial \(x^{2}-4\) can be expressed as \((x-2)(x+2)\) since it's a difference of squares. The operation \(\frac{x^{2}-4}{x-2}\) then simplifies to \(x+2\) after canceling out \(x-2\) in the numerator and the denominator. Similarly, the denominator in the second fraction, \(4x-8\), can be factored as \(4(x-2)\), then \(\frac{x+2}{4x-8}\) simplifies to \(\frac{1}{4}\) after canceling out \(x+2\) and \(x-2\).
02

Convert the Division to Multiplication

The operation \(\frac{x^{2}-4}{x-2} \div \frac{x+2}{4x-8}\) is equivalent to \((x+2) \times \frac{1}{4}\) after converting the division to multiplication and using the reciprocal of the second term.
03

Multiply

After the conversion, the multiplication operation becomes simple. The term \((x+2) \times \frac{1}{4}\) simplifies further to \(\frac{1}{4}x + \frac{1}{2}\).

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 convert from scientific to decimal notation and give an example.

Factor completely. $$ x^{2 n}+6 x^{n}+8 $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$5^{2} \cdot 5^{-2}>2^{5} \cdot 2^{-5}$$

How do you know if a number is written in scientific notation?

Simplify by reducing the index of the radical. $$\sqrt[12]{x^{4} y^{8}}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.