/*! 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 86 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 86

Perform the indicated operations. Simplify the result, if possible. $$\left(4-\frac{3}{x+2}\right)\left(1+\frac{5}{x-1}\right)$$

Short Answer

Expert verified
\( \frac{4x^{2}+25x+34}{x^{2}+x-2} \)

Step by step solution

01

Apply distributive law

Apply the distributive law \(a(b + c) = ab + ac\) to both terms of the first bracket: \[(4-\frac{3}{x+2})(1+\frac{5}{x-1}) = 4 * 1 + 4 * \frac{5}{x-1} - \frac{3}{x+2} * 1 -\frac{3}{x+2} * \frac{5}{x-1}\]
02

Simplify

Re-arrange and simplify the obtained terms:\[4 + 20*\frac{1}{x-1} - 3*\frac{1}{x+2} - 15*\frac{1}{(x+2)(x-1)}\]
03

Simplify further

The fractions in the equation have different denominators, so before we can add or subtract them, we need to find a common denominator. The common denominator of \(x-1\), \(x+2\) and \((x+2)(x-1)\) is \((x+2)(x-1)\). So convert all terms into fractions with that denominator:\[4 + \frac{20(x+2)}{(x+2)(x-1)} - \frac{3(x-1)}{(x+2)(x-1)} - \frac{15}{(x+2)(x-1)}\]
04

Combine like terms

Now all terms have the same denominator, so they can be combined:\[\frac{4(x+2)(x-1) + 20*(x+2) - 3*(x-1) -15}{(x+2)(x-1)} \]
05

Simplify final expression

Simplify the resulting expression by calculating all terms in the numerator:\[\frac{4x^{2}+8x-4 + 20x +40 - 3x +3 - 15}{x^{2} + x -2}\]Then combine like terms in the numerator:\[\frac{4x^{2}+25x+34}{x^{2} + x -2}\]

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

The average rate on a round-trip commute having a one-way distance \(d\) is given by the complex rational expression $$\frac{2 d}{\frac{d}{r_{1}}+\frac{d}{r_{2}}}$$ in which \(r_{1}\) and \(r_{2}\) are the average rates on the outgoing and return trips, respectively. Simplify the expression. Then find your average rate if you drive to campus averaging 40 miles per hour and return home on the same route averaging 30 miles per hour. Explain why the answer is not 35 miles per hour.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. You are choosing between two texting plans. Plan A has a monthly fee of \(\$ 15\) with a charge of \(\$ 0.08\) per text. Plan \(\mathbf{B}\) has a monthly fee of \(\$ 3\) with a charge of \(\$ 0.12\) per text. How many text messages in a month make plan A the better deal?

What is a rational expression?

The rational expression $$\frac{130 x}{100-x}$$ describes the cost, in millions of dollars, to inoculate \(x\) percent of the population against a particular strain of flu. a. Evaluate the expression for \(x=40, x=80,\) and \(x=90\) Describe the meaning of each evaluation in terms of percentage inoculated and cost. b. For what value of \(x\) is the expression undefined? c. What happens to the cost as \(x\) approaches \(100 \% ?\) How can you interpret this observation?

Perform the indicated operations. Simplify the result, if possible. $$\frac{a b}{a^{2}+a b+b^{2}}+\left(\frac{a c-a d-b c+b d}{a c-a d+b c-b d} \div \frac{a^{3}-b^{3}}{a^{3}+b^{3}}\right)$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.