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- Elementary algebra
- Rational expressions
- Summary of key concepts
<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>This module presents a summary of the key concepts of the chapter "Rational Expressions".</para>
Summary of key concepts
Rational expression (
[link] )
A
rational expression is an algebraic expression that can be written as the quotient of two polynomials. An example of a rational expression is
Domain of a rational expression (
[link] )
The
domain of a rational expression is the collection of values for which the raticlnal expression is defined. These values can be found by determining the values that will not produce zero in the denominator of the expression.
The domain of
is the collection of all numbers except
.
Equality property of fraction (
[link] )
- If
, then
.
- If
, then
.
Negative property of fractions (
[link] )
Reducing a rational expression (
[link] )
- Factor the numerator and denominator completely.
- Divide the numerator and denominator by any factors they have in common.
Common cancelling error (
[link] )
Since
is not a common factor, it cannot be cancelled.
Multiplying rational expressions (
[link] )
- Factor all numerators and denominators.
- Reduce to lowest terms first by dividing out all common factors.
- Multiply numerators together.
- Multiply denominators together.
It will be more convenient to leave the denominator in factored form.
Division of rational expressions (
[link] )
Building rational expressions (
[link] )
Building rational expressions is exactly the opposite of reducing rational expressions. It is often useful in adding or subtracting rational expressions.
The building factor may be determined by dividing the original denominator into the new denominator. The quotient will be the building factor. It is this factor that will multiply the original numerator.
Least common denominator lcd (
[link] )
The LCD is the polynomial of least degree divisible by each denominator. It is found as follows:
- Factor each denominator. Use exponents for repeated factors.
- Write each
different factor that appears. If a factor appears more than once, use only the factor with the highest exponent.
- The LCD is the product of the factors written in step 2.
Fundamental rule for adding or subtracting rational expressions (
[link] )
To add or subtract rational expressions conveniently, they should have the same denominator.
Adding and subtracting rational expressions (
[link] )
Note that we combine
only the numerators.
Rational equation (
[link] )
A
rational equation is a statement that two rational expressions are equal.
Clearing an equation of fractions (
[link] )
To clear an equation of fractions, multiply both sides of the equation by the LCD. This amounts to multiplying every term by the LCD.
Solving a rational equation (
[link] )
- Determine all values that must be excluded as solutions by finding the values that produce zero in the denominator.
- Clear the equation of fractions by multiplying every term by the LCD.
- Solve this nonfractional equation for the variable. Check to see if any of these potential solutions are excluded values.
- Check the solution by substitution.
A potential solution that has been excluded because it creates an undefined expression (perhaps, division by zero) is called an
extraneous solution.
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
Organ Systems Of The Human Body (Continued)
Organ Systems Of The Human Body (Continued)
what's lochia albra
Kizito
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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