What defines an algebraic fraction

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An algebraic fraction, or rational function, is defined as one polynomial divided by another, which can involve multiple variables. The discussion highlights confusion around simplifying fractions, particularly with the example of (a^2 - 10a + 21)/(a^2 - 11a + 28). Participants clarify that to simplify, one must factor both the numerator and denominator, leading to a reduced form. The original poster struggles with understanding how to cancel terms correctly, especially when dealing with an odd number of variables. Ultimately, the simplification process results in a valid algebraic expression, confirming the textbook's solution.
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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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