/*! 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 simplified expression is \(\frac{-3}{x(x+1)}\).

Step by step solution

01

Identifying the common denominator

The common denominator needs to be a multiple of both \(x+1\) and \(x\). Since these two expressions are relatively prime (i.e., they don't share factors), their product, \(x(x+1)\), is a common denominator.
02

Adjusting the fractions to have a common denominator

You can rewrite \(\frac{3}{x+1}\) as \(\frac{3x}{x(x+1)}\) and \(\frac{3}{x}\) as \(\frac{3(x+1)}{x(x+1)}\), each time multiplying the numerator and denominator of the fraction by the missing expression from the common denominator. So \(\frac{3}{x+1}-\frac{3}{x}\) becomes \(\frac{3x}{x(x+1)} - \frac{3(x+1)}{x(x+1)}\).
03

Subtraction

Subtract the new expressions. \[\frac{3x}{x(x+1)} - \frac{3(x+1)}{x(x+1)} = \frac{3x - 3(x+1)}{x(x+1)}\] This simplifies to \(\frac{3x - 3x - 3}{x(x+1)}\) or \(\frac{-3}{x(x+1)}\).

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

Rewrite each expression without absolute value bars. $$|300|$$

Determine whether each statement in Exercises 43鈥�50 is true or false. $$-13 \leq-2$$

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

$$\text { factor completely.}$$ $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$

Find the intersection of the sets. $$\\{a, b, c, d\\} \cap \varnothing$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.