/*! 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 108 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 108

Perform the indicated operations. $$(x-y)^{-1}+(x-y)^{-2}$$

Short Answer

Expert verified
The simplified form of the given expression is \(\frac{(x-y)+1}{(x-y)^2}\)

Step by step solution

01

Understanding the Negative Exponent Rule

In mathematics, a negative exponent refers to the reciprocal (or 'flip') of the base. Thus, \((x-y)^{-1}\) becomes \(\frac{1}{x-y}\), and \((x-y)^{-2}\) becomes \(\frac{1}{(x-y)^2}\). Therefore, the expression simplifies to: \(\frac{1}{x-y}+\frac{1}{(x-y)^2}\).
02

Finding a Common Denominator

To add two fractions, a common denominator (same bottom number) is needed. The common denominator between \((x-y)\) and \((x-y)^2\) is \((x-y)^2\). Thus, the first fraction is multiplied by \((x-y)\) at the top and bottom. The expression then becomes: \(\frac{(x-y)}{(x-y)^2}+\frac{1}{(x-y)^2}\).
03

Addition of fractions

Since the denominators of both fractions are the same, the fractions can now be added by adding the numerators and keeping the denominator constant. This gives the final simplified expression: \(\frac{(x-y)+1}{(x-y)^2}\).

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

Factor completely. $$ -x^{2}-4 x+5 $$

Simplify using properties of exponents. $$\frac{\left(3 y^{\frac{1}{4}}\right)^{3}}{y^{\frac{1}{12}}}$$

The early Greeks believed that the most pleasing of all rectangles were golden rectangles, whose ratio of width to height is $$\frac{w}{h}=\frac{2}{\sqrt{5}-1}$$ The Parthenon at Athens fits into a golden rectangle once the triangular pediment is reconstructed. (IMAGE CANT COPY) Rationalize the denominator of the golden ratio. Then use a calculator and find the ratio of width to height, correct to the nearest hundredth, in golden rectangles.

Simplify by reducing the index of the radical. $$\sqrt[9]{x^{6} y^{3}}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.