/*! 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 32 Multiply or divide as indicated.... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Multiply or divide as indicated. $$\frac{x^{3}-25 x}{4 x^{2}} \cdot \frac{2 x^{2}-2}{x^{2}-6 x+5} \div \frac{x^{2}+5 x}{7 x+7}$$

Short Answer

Expert verified
The simplified form of the given expression is \( \frac{x}{2} \)

Step by step solution

01

Factorize the Numerators and Denominators

The factorized form is given by: \( \frac{(x-5)(x^{2}+5)}{4x(x+1)} \cdot \frac{2x(x-1)}{(x-5)(x-1)} \div \frac{x(x+5)}{7(x+1)} \)
02

Multiply and Divide as indicated

Perform multiplication and division from left to right: \( = \frac{(x-5)(x^{2}+5)(2x(x-1))}{4x(x+1)*(x-5)(x-1)} \div \frac{x(x+5)}{7(x+1)} =\frac{(x-5)(x^{2}+5)(2x(x-1))(7)(x+1)}{4x(x+1)*(x-5)(x-1)x(x+5)} \)
03

Cancel out Common Factors

Cancel out common factors on top and bottom to simplify: \( =\frac{2x^{2}}{4x} = \frac{x}{2} \)

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 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.