/*! 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 63 $$\text { In Exercises } 61-68, ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 63

$$\text { In Exercises } 61-68, \text { solve or simplify, whichever is appropriate.}$$ $$\frac{x^{2}+4 x-2}{x^{2}-2 x-8}-1-\frac{4}{x-4}$$

Short Answer

Expert verified
\(- \frac{x^{2}-6x-6}{(x - 4)(x + 2)}\)

Step by step solution

01

Factorize the Polynomials

The second polynomial in the denominator \(x^{2}-2x-8\) can be factored as \((x-4)(x+2)\). The first fraction becomes \(\frac{x^{2}+4x-2}{(x-4)(x+2)}\). The expression now can be rewritten as \(\frac{x^{2}+4x-2}{(x-4)(x+2)} - 1 - \frac{4}{x-4}\).
02

Find a Common Denominator

You now need to find a common denominator for the three terms to combine them. The common denominator of \((x-4)(x+2)\), \(x-4\), and 1 would be \((x-4)(x+2)\). So, the whole expression is transformed into \(\frac{x^{2}+4x-2}{(x-4)(x+2)} - \frac{(x-4)(x+2)}{(x-4)(x+2)} - \frac{4(x+2)}{(x-4)(x+2)}\).
03

Combine the Fractions

Now combine all the terms over the single denominator \((x-4)(x+2)\), this results in \(\frac{x^{2}+4x-2 - (x-4)(x+2) - 4(x+2)}{(x-4)(x+2)}\).
04

Simplify the Numerator

Expand and simplify the numerator: \(x^{2}+4x-2 - (x^{2}-2x-8) - 4x-8\), eventually becomes: \(-x^{2}+6x+6\).
05

Final Result

Replacing the simplified numerator in the fraction you get \(- \frac{x^{2}-6x-6}{(x - 4)(x + 2)}\) as the final result.

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

In Exercises \(83-86,\) determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve the equation \(\frac{6}{x+3}=\frac{4}{x-3}\) by multiplying both sides by the LCD.

Explain how to add rational expressions that have different denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.

Exercises \(123-125\) will help you prepare for the material covered in the next section. Multiply and simplify: \(\quad x y\left(\frac{1}{x}+\frac{1}{y}\right)\)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{y}{y^{2}+2 y+1}+\frac{4}{y^{2}+5 y+4}$$

In Palo Alto, California, a government agency ordered computer-related companies to contribute to a pool of money to clean up underground water supplies. (The companies had stored toxic chemicals in leaking underground containers.) The formula $$ C=\frac{2 x}{100-x} $$ models the cost, \(C\), in millions of dollars, for removing \(x\) percent of the contaminants. Use this mathematical model to solve Exercises \(71-72\). What percentage of the contaminants can be removed for \(\$ 2\) million?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Geometry

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.