Finding the HCF of Numerator and Denominator

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Homework Help Overview

The discussion revolves around finding the highest common factor (HCF) of the numerator and denominator in rational expressions, particularly in the context of simplifying fractions that may involve multiple variables.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses a desire to identify whether a numerator and denominator share a common factor to simplify problems more efficiently. Some participants suggest understanding common divisibility rules and complete factorization as potential methods. Others inquire about resources for learning these rules and clarify the context of the discussion, particularly regarding the complexity of the expressions involved.

Discussion Status

The conversation is ongoing, with participants exploring various methods for factoring and simplifying rational expressions. There is a recognition of the need for foundational knowledge in divisibility and factorization, and some guidance has been offered regarding approaches to take.

Contextual Notes

Participants mention the complexity of the expressions being discussed, including those with multiple variables, which may require more advanced techniques for factorization. There is also a note on the potential difference in understanding based on educational background.

Miike012
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After finding the simple factors in the numerator and denominator... Is there any way of knowing if the numerator and denominator has a HCF?

I think this would be very beneficial for me to know because if I want to simplify a "hard problem" into s simpler equation I can. However when I try to find HCF in some problems I find my self waisting time because most of the problems don't have a HCF, therefore can not be simplified.

So is there a way to quickley decide if there is an hcf? Are there any methods to doing this?

thank you.
Mike
 
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This is mostly a matter of knowing common divisibility rules and knowing how to, if possible, completely factor numbers. One of the goals is to know or find out if a fraction is already simplified --- as you found, if no common factors occur in both numerator and denominator, the fraction is simplified (assuming your interest is not about "mixed number" versus improper fraction).
 
Im not familliar with all of the divisibility rules... where can I find them?
 
Miike012 said:
Im not familliar with all of the divisibility rules... where can I find them?

I assumed your point of view was Basic Mathematics as in elementary basic education. Any beginning Arithmetic or other Basic Mathematics textbook would include divisibility rules. Is your point of view, instead something more advanced?
 
Im talking about a ratio that consists of more than one variable..
example..
(xy^5 - x^3 + z -10) / ( xyz 10x -9y ^2)...
I just made this up... but this is what I am talking about...
 
You want to factor rational expressions, so now we see. Use grouping, inspection, looking for any common factors among the numerator terms or the denominator terms; depending on the expressions present maybe try Rational Roots Theorem, if expressions are of the right form maybe try polynomial division, or if practical synthetic division. Some parts of Intermediate and College Algebra are dedicated to what you asked.
 

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