/*! 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 54 Add or subtract as indicated. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 54

Add or subtract as indicated. $$\frac{x}{x^{2}-2 x-24}-\frac{x}{x^{2}-7 x+6}$$

Short Answer

Expert verified
The simplified form of the expression is \(-5x/(x-6)(x+4)(x-1)\)

Step by step solution

01

Factor the Denominators

Split the quadratic expressions of each factor into two binomial expressions: \(x^{2}-2x-24=(x-6)(x+4)\) and \(x^{2}-7x+6=(x-6)(x-1)\). So, we rewrite the expression as \[\frac{x}{(x-6)(x+4)}-\frac{x}{(x-6)(x-1)}\].
02

Find the Least Common Denominator

As \(x-6\) is already a common factor, hence the least common denominator (LCD) for the two fractions will be \((x-6)(x+4)(x-1)\).
03

Rewrite the Fractions with the LCD

We rewrite the fractions using the LCD. The first fraction lacks the \((x-1)\) term, and the second fraction lacks the \((x+4)\) term in the denominator. So \[\frac{x}{(x-6)(x+4)}-\frac{x}{(x-6)(x-1)} = \frac{x(x-1)}{(x-6)(x+4)(x-1)}- \frac{x(x+4)}{(x-6)(x+4)(x-1)}\].
04

Subtract the Fractions

Now subtract the fractions: \[\frac{x(x-1)}{(x-6)(x+4)(x-1)}- \frac{x(x+4)}{(x-6)(x+4)(x-1)} = \frac{x^2 - x - x^2 - 4x}{(x-6)(x+4)(x-1)}\] Simplify to get: \(-5x/(x-6)(x+4)(x-1)\)

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

Find the union of the sets. $$\\{1,3,5,7\\} \cup\\{2,4,6,8,10\\}$$

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{5(x+2)}{2 x-14}, \text { for } x=10$$

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{7(x-3)}{2 x-16}, \text { for } x=9$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\\{-7,-0 . \overline{6}, 0, \sqrt{49}, \sqrt{50}\\}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.