What defines an algebraic fraction

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Homework Help Overview

The discussion revolves around the definition and simplification of algebraic fractions, particularly focusing on the characteristics of the numerator and denominator. Participants are exploring examples and textbook references to clarify their understanding.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to define algebraic fractions and question how to simplify them. There are discussions about specific examples, such as the fraction 3/2x and the expression a^2-10a+21/a^2-11a+28, with some participants expressing confusion over the simplification process and the resulting forms.

Discussion Status

The discussion is ongoing, with participants sharing their interpretations and attempting to clarify the steps involved in simplifying algebraic fractions. Some guidance has been offered regarding the need to factor expressions, but there is no explicit consensus on the methods or outcomes.

Contextual Notes

Participants are working within the constraints of homework assignments, which may limit the information they can access or the methods they can use. There is also mention of textbook examples that may not be clear to all participants.

ramstin
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O.k. I am trying to figure out what defines an algebraic fraction. I know it has something to do with the denominator but for the life of me I can not make any sense out of my textbook examples. Like 3/2x = 0 I guess 3/x*x = 3 divided by no actual number which would be zero but that is the best I can work out after 4 hours of trying to do this section of my homework.
 
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ramstin said:
O.k. I am trying to figure out what defines an algebraic fraction. I know it has something to do with the denominator but for the life of me I can not make any sense out of my textbook examples. Like 3/2x = 0 I guess 3/x*x = 3 divided by no actual number which would be zero but that is the best I can work out after 4 hours of trying to do this section of my homework.

Does this link help?

http://www.themathpage.com/Alg/multiply-algebraic-fractions.htm
 
An algebraic fraction, also caled a rational function, is one polynomial divided by another. The polynomials may be of several variables.
 
O.k. if I have a^2-10a+21/a^2-11a+28 I then get 21/-1a+28 and then 3/-a+4 but my book says I should get a-3/a-4 How did that happen?
 
ramstin said:
O.k. if I have a^2-10a+21/a^2-11a+28 I then get 21/-1a+28 and then 3/-a+4 but my book says I should get a-3/a-4 How did that happen?

They are asking you to simplify the fraction. Factor the numerator and denominator and simplify.

(PS: Their answer is right.)
 
even with simplifying how do you get an a on both sides when their is an odd number of them to begin with?
 
ramstin said:
even with simplifying how do you get an a on both sides when their is an odd number of them to begin with?

What both sides? You have an expression that is a fraction. You have a numerator and you have a denominator.

After you have factored both equations (top and bottom) you still have an expression that is still an algebraic fraction. When the like terms are canceled top and bottom, you are still left with an algebraic expression - only it's the answer given.
 

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