/*! 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 93 Explain how to find the least co... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 93

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 of the denominators of expressions \(x^{2}-100\) and \(x^{2}-20 x+100\) is \((x+10)(x-10)^{2}\).

Step by step solution

01

Factorize the denominators.

Factorize the denominators to simplify the equations. The expression \(x^{2}-100\) can be factorized into \((x+10)(x-10)\), using the difference of squares formula (a虏 - b虏 = (a + b)(a - b)). The expression \(x^{2}-20 x+100\) can be factorized as \((x-10)^{2}\), using the square of a binomial formula (a虏 - 2ab + b虏 = (a - b)虏).
02

Find the common factors.

Determine the common factor from each factorized denominator. In this case, the common factor is \((x-10)\) since it appears in both denominators when factorized.
03

Determine the least common denominator.

Finally, build the least common denominator, incorporating all the factors from both denominators, only duplicating the common factors once. Here, the factors are \((x+10)\), \((x-10)\), and \((x-10)\) again from the square. We only count \((x-10)\) once, so the least common denominator is \((x+10)(x-10)^{2}\).

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

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

Use Einstein's special-relativity equation $$R_{a}=R_{f} \sqrt{1-\left(\frac{v}{c}\right)^{2}}$$ described in the Blitzer Bonus on page 47,to solve this exercise. You are moving at \(90 \%\) of the speed of light. Substitute 0.9c for v, your velocity, in the equation. What is your aging rate, correct to two decimal places, relative to a friend on Earth? If you are gone for 44 weeks, approximately how many weeks have passed for your friend?

Explain how to factor the difference of two squares. Provide an example with your explanation.

Factor and simplify each algebraic expression. $$-8(4 x+3)^{-2}+10(5 x+1)(4 x+3)^{-1}$$

Factor and simplify each algebraic expression. $$\left(x^{2}+4\right)^{\frac{1}{2}}+\left(x^{2}+4\right)^{\frac{7}{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.