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<para>This module is from<link document="col10614">Elementary Algebra</link>by Denny Burzynski and Wade Ellis, Jr.</para><para>A detailed study of arithmetic operations with rational expressions is presented in this chapter, beginning with the definition of a rational expression and then proceeding immediately to a discussion of the domain. The process of reducing a rational expression and illustrations of multiplying, dividing, adding, and subtracting rational expressions are also included. Since the operations of addition and subtraction can cause the most difficulty, they are given particular attention. We have tried to make the written explanation of the examples clearer by using a "freeze frame" approach, which walks the student through the operation step by step.</para><para>The five-step method of solving applied problems is included in this chapter to show the problem-solving approach to number problems, work problems, and geometry problems. The chapter also illustrates simplification of complex rational expressions, using the combine-divide method and the LCD-multiply-divide method.</para><para>Objectives of this module: be able to multiply and divide rational expressions.</para>

Overview

  • Multiplication Of Rational Expressions
  • Division Of Rational Expressions

Multiplication of rational expressions

Rational expressions are multiplied together in much the same way that arithmetic fractions are multiplied together. To multiply rational numbers, we do the following:

Method for Multiplying Rational Numbers
  1. Reduce each fraction to lowest terms.
  2. Multiply the numerators together.
  3. Multiply the denominators together.

Rational expressions are multiplied together using exactly the same three steps. Since rational expressions tend to be longer than arithmetic fractions, we can simplify the multiplication process by adding one more step.

Method for Multiplying Rational Expressions
  1. Factor all numerators and denominators.
  2. Reduce to lowest terms first by dividing out all common factors. (It is perfectly legitimate to cancel the numerator of one fraction with the denominator of another.)
  3. Multiply numerators together.
  4. Multiply denominators. It is often convenient, but not necessary, to leave denominators in factored form.

Sample set a

Perform the following multiplications.

3 4 · 1 2 = 3 · 1 4 · 2 = 3 8

8 9 · 1 6 = 8 4 9 · 1 6 3 = 4 · 1 9 · 3 = 4 27

3 x 5 y · 7 12 y = 3 1 x 5 y · 7 12 4 y = x · 7 5 y · 4 y = 7 x 20 y 2

x + 4 x - 2 · x + 7 x + 4 Divide out the common factor  x + 4. x + 4 x - 2 · x + 7 x + 4 Multiply numerators and denominators together . x + 7 x - 2

x 2 + x - 6 x 2 - 4 x + 3 · x 2 - 2 x - 3 x 2 + 4 x - 12 . Factor . ( x + 3 ) ( x - 2 ) ( x - 3 ) ( x - 1 ) · ( x - 3 ) ( x + 1 ) ( x + 6 ) ( x - 2 ) Divide out the common factors  x - 2  and  x - 3. ( x + 3 ) ( x - 2 ) ( x - 3 ) ( x - 1 ) · ( x - 3 ) ( x + 1 ) ( x + 6 ) ( x - 2 ) Multiply . ( x + 3 ) ( x + 1 ) ( x - 1 ) ( x + 6 ) or x 2 + 4 x + 3 ( x - 1 ) ( x + 6 ) or x 2 + 4 x + 3 x 2 + 5 x - 6 Each of these three forms is an acceptable form of the same answer .

2 x + 6 8 x - 16 · x 2 - 4 x 2 - x - 12 . Factor . 2 ( x + 3 ) 8 ( x - 2 ) · ( x + 2 ) ( x - 2 ) ( x - 4 ) ( x + 3 ) Divide out the common factors 2,  x + 3  and  x - 2. 2 1 ( x + 3 ) 8 4 ( x - 2 ) · ( x + 2 ) ( x - 2 ) ( x + 3 ) ( x - 4 ) Multiply . x + 2 4 ( x - 4 ) or x + 2 4 x - 16 Both these forms are acceptable forms of the same answer .

3 x 2 · x + 7 x - 5 . Rewrite  3 x 2  as  3 x 2 1 . 3 x 2 1 · x + 7 x - 5 Multiply . 3 x 2 ( x + 7 ) x - 5

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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Source:  OpenStax, Algebra ii for the community college. OpenStax CNX. Jul 03, 2014 Download for free at http://cnx.org/content/col11671/1.1
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