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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

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
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
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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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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