/*! 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 8 Multiply as indicated. $$\frac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 8

Multiply as indicated. $$\frac{x-2}{x+9} \cdot \frac{5 x+45}{2 x-4}$$

Short Answer

Expert verified
The result of the multiplication is \(\frac{5}{2}\).

Step by step solution

01

Simplify the Fractions

Each of the fractions can be simplified. The first fraction would remain the same while the second fraction can be simplified. For \(\frac{5x+45}{2x-4}\), take 5 out as a common factor from the numerator and 2 from the denominator. So it will be \(\frac{5(x+9)}{2(x-2)}\). Now our expression becomes, \(\frac{x-2}{x+9} \cdot \frac{5(x+9)}{2(x-2)}\).
02

Multiply the Fractions

Multiply across as you would with simple fractions - multiply numerator with numerator and denominator with denominator. It's done this way: \(\frac{(x-2)\cdot 5(x+9)}{(x+9)\cdot 2(x-2)}\).
03

Simplify the Result

Observe that both the numerator and the denominator of the equation have common factors, specifically (x-2) and (x+9). Therefore, we can simplify the equation by removing these common factors. The final result of the multiplication operation is \(\frac{5}{2}\).

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

Explain how to add rational expressions when denominators are opposites. Use an example to support your explanation.

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6 x+7}{x-6}+\frac{3 x}{6-x}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-7}{y^{2}-16}+\frac{7-y}{16-y^{2}}$$

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?

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

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure 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.