/*! 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 71 Add or subtract as indicated. Si... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 71

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x+3}{x^{2}+x-2}-\frac{2}{x^{2}-1}$$

Short Answer

Expert verified
The simplified expression is \(\frac{x^2 + 2x - 1}{(x-1)(x+2)(x+1)}\).

Step by step solution

01

Factor denominators

Factor the denominators \(x^{2}+x-2\) and \(x^{2}-1\). The factored form of \(x^{2}+x-2\) is \((x-1)(x+2)\) and of \(x^{2}-1\) is \((x-1)(x+1)\).
02

Find common denominator

Identify the common denominator for the two expressions. This would be the product of unique factors, which is \((x-1)(x+2)(x+1)\).
03

Rewrite the expression

Rewrite each fraction with the common denominator. Multiply each term by needed factors. The expression becomes \[\frac{(x+3)(x+1)}{(x-1)(x+2)(x+1)} - \frac{2(x+2)}{(x-1)(x+2)(x+1)}\].
04

Simplify

Subtract the fractions, performing the operation in the numerators as the denominator is the same: \[\frac{(x+3)(x+1) - 2(x+2)}{(x-1)(x+2)(x+1)}\].
05

Further simplify the numerator

Expand and simplify the numerator to get \(\frac{x^2 + 2x - 1}{(x-1)(x+2)(x+1)}\).
06

Check if it can be factored

Check to see if the new numerator can be factored. It can't, as there are no factors of -1 that combine to make 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

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{3 x+6}{2}-\frac{x}{2}=x+3$$

If you know how many hours it takes for you to do a job, explain how to find the fractional part of the job you can complete in \(x\) hours.

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{b}{a c+a d-b c-b d}-\frac{a}{a c+a d-b c-b d}$$

Use similar triangles to solve. A person who is 5 feet tall is standing 80 feet from the base of a tree. The tree casts an 86 -foot shadow. The person's shadow is 6 feet in length. What is the tree's height? (IMAGE CANNOT COPY)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 x+3}{x^{2}-x-30}+\frac{x-2}{30+x-x^{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

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.