/*! 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 76 Add or subtract as indicated. Si... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 76

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x+7}{4 x+12}+\frac{x}{9-x^{2}}$$

Short Answer

Expert verified
The simplified sum of the two fractions is \[\frac{(x+7)(9-x^{2}) + x(4x+12)}{(4x+12)(9-x^{2})}\]

Step by step solution

01

Identify Common Denominator

In this scenario, the common denominator is the least common multiple (LCM) of \(4x + 12\) and \(9 - x^{2}\). The LCM for these two expressions is their product, i.e., \((4x + 12)(9 - x^{2})\) since they don't have common root.
02

Rewrite Fractions

Rewrite each fraction with the new denominator: \[\frac{x+7}{4x+12} * \frac{9-x^{2}}{9-x^{2}} = \frac{(x+7)(9-x^{2})}{(4x+12)(9-x^{2})}\] and \[\frac{x}{9-x^{2}} * \frac{4x+12}{4x+12} = \frac{x(4x+12)}{(4x+12)(9-x^{2})}\]
03

Perform Addition

Since these fractions now have the same denominator, they can be added directly: \[\frac{(x+7)(9-x^{2}) + x(4x+12)}{(4x+12)(9-x^{2})}\]
04

Simplify

The expression can then be simplified (if applicable). In this case, it is not possible to simplify any further, since no factors are common to the numerator and the denominator.

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

Two investments have interest rates that differ by \(1 \% .\) An investment for 1 year at the lower rate earns 175 . The same principal invested for a year at the higher rate earns 200 dollars . What are the two interest rates?

What are similar triangles?

Describe two similarities between the following problems: $$ \frac{3}{8}+\frac{1}{8} \text { and } \frac{x}{x^{2}-1}+\frac{1}{x^{2}-1} $$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{(y-3)(y+2)}{(y+1)(y-4)}-\frac{(y+2)(y+3)}{(y+1)(4-y)}-\frac{(y+5)(y-1)}{(y+1)(4-y)}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4}{x-3}+\frac{2}{3-x}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.