/*! 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 15 Multiply as indicated. $$\frac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 15

Multiply as indicated. $$\frac{y^{2}-7 y-30}{y^{2}-6 y-40} \cdot \frac{2 y^{2}+5 y+2}{2 y^{2}+7 y+3}$$

Short Answer

Expert verified
The result of the multiplication is \(\frac{y^{3}+5y^{2}-19y-43}{y^{3}+7y^{2}-28y-81}\)

Step by step solution

01

Set up the problem

First, set up the problem with the two fractions that need to be multiplied. This is done by multiplying the numerators together and the denominators together. So, we have \((y^{2}-7y-30)\cdot (2y^{2}+5y+2)\) over \((y^{2}-6y-40)\cdot (2y^{2} +7y+3)\)
02

Multiply the numerators

Multiply the numerators together. This should produce the polynomial: \(2y^{4}+5y^{3}-19y^{2}-86y-60\)
03

Multiply the denominators

Multiply the denominators together. This results in the polynomial: \(2y^{4}+7y^{3}-28y^{2}-162y-120\)
04

Insert the results into the fraction

Place the result from the numerators and denominators multiplication into the fraction. It should be \(\frac{2y^{4}+5y^{3}-19y^{2}-86y-60}{2y^{4}+7y^{3}-28y^{2}-162y-120}\)
05

Cancel common terms

In this fraction, \(2y^4\) is common in the numerator and the denominator. Also, the constants -60 and -120 are common. It can be reduced to \(\frac{y^{3}+5y^{2}-19y-43}{y^{3}+7y^{2}-28y-81}\). This is the simplest form of the fraction that can be obtained.

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

A snowstorm causes a bus driver to decrease the usual average rate along a 60 -mile route by 15 miles per hour. As a result, the bus takes two hours longer than usual to complete the route. At what average rate does the bus usually cover the 60 -mile route?

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4-x}{x-9}-\frac{3 x-8}{9-x}$$

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

After adding \(\frac{3 x+1}{4}\) and \(\frac{x+2}{4},\) I simplified the sum by dividing the numerator and the denominator by 4 I use similar procedures to find each of the following sums: $$ \frac{3}{8}+\frac{1}{8} \text { and } \frac{x}{x^{2}-1}+\frac{1}{x^{2}-1} $$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{10}{x-2}-\frac{6}{2-x}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.