/*! 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 43 Add or subtract as indicated. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 43

Add or subtract as indicated. $$\frac{3}{x+1}-\frac{3}{x}$$

Short Answer

Expert verified
The answer is \(-\frac{3}{x(x+1)}\).

Step by step solution

01

Find the Least Common Denominator (LCD)

The denominators are \(x+1\) and \(x\). The Least Common Denominator (LCD) is a product of the two values, so the LCD is \(x(x+1)\).
02

Express the fractions using the LCD

Each fraction must be rewritten with the LCD as the denominator. Then the fractions become: \(\frac{3x}{x(x+1)}\) and \(\frac{3(x+1)}{x(x+1)}\).
03

Subtract the fractions

Now, subtract the second fraction from the first while keeping the same denominator: \(\frac{3x-3(x+1)}{x(x+1)} = \frac{3x - 3x - 3}{x(x+1)}\).
04

Simplify the fraction

After subtracting the parts with similar variables you get: \(-\frac{3}{x(x+1)}\).

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

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A truck can be rented from Basic Rental for \(\$ 50\) per day plus \(\$ 0.20\) per mile. Continental charges \(\$ 20\) per day plus \(\$ 0.50\) per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for Basic Rental a better deal than Continental's?

Find \(b\) such that \(\frac{7 x+4}{b}+13=x\) will have a solution set given by \(\\{-6\\}\).

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Decision 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.