/*! 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 103 Explain how to find the least co... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 103

Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\)

Short Answer

Expert verified
The least common denominator for the fractions with denominators \(x^{2}-100\) and \(x^{2}-20x+100\) is \((x+10) (x-10)^{2}\).

Step by step solution

01

Factorize the denominators

The first step is to factorize each of the denominators. For \(x^{2}-100\), this is a difference of two squares and thus can be factored to \((x+10) (x-10)\). \(x^{2}-20x+100\) on the other hand, is a perfect square trinomial and can be factored to \((x-10)^{2}\).
02

Identify common factors

Once the factorization is done, identify the factors common to both denominators. Here, the common factor is \((x-10)\).
03

Find the LCD

The LCD will be all the unique factors from both denominators, with each factor raised to the highest power it appears in either denominator. This translates to \((x+10) (x-10)^{2}\).

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

What is a rational equation?

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x^{2}-10 x+25}-\frac{x-4}{2 x-10}$$

In Exercises \(83-86,\) determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve the equation \(\frac{6}{x+3}=\frac{4}{x-3}\) by multiplying both sides by the LCD.

Will help you prepare for the material covered in the first section of the next chapter. Here are two sets of ordered pairs: $$\text { set } 1:\\{(1,5),(2,5)\\}$$ set \(2:[(5,1),(5,2)]\) In which set is each \(x\) -coordinate paired with only one \(y\) -coordinate?

Will help you prepare for the material covered in the first section of the next chapter. Evaluate \(5 x+7\) for \(x=a+h\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics 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.