Algebraic expressions - simplifying

  • Context: High School 
  • Thread starter Thread starter Rationalist
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    Expressions Simplifying
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Discussion Overview

The discussion revolves around simplifying a complex algebraic expression involving multiple fractions. Participants are exploring methods to combine these fractions effectively, particularly in the context of preparing for the GRE.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses concern about the complexity of the expression and seeks guidance on simplification methods.
  • Another participant notes a specific algebraic identity regarding the relationship between (b - a) and (a - b) that may aid in simplification.
  • A suggestion is made to rewrite the fractions with a common denominator of (a-b)(a-c)(b-c) to facilitate addition.
  • One participant encourages a hands-on approach, suggesting that one should not hesitate to write down the work involved, regardless of the potential complexity of the result.

Areas of Agreement / Disagreement

Participants present various methods and perspectives on simplifying the expression, but no consensus is reached on a single approach or solution.

Contextual Notes

Participants do not clarify specific assumptions or limitations regarding the variables involved or the steps required for simplification.

Who May Find This Useful

Individuals preparing for standardized tests like the GRE, as well as those looking to improve their algebraic manipulation skills.

Rationalist
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Hi all,

I'm retaking the GRE soon and I keep making stupid algebra mistakes in my calculus problems so I'm going through a textbook from 1965 that is helpful but has me stumped on some problems. I hope someone can steer me in the right direction.

1/(a-b)(a-c) + 1/(c-a)(c-b) + 1/(b-a)(b-c)

Is there a way to simplify this? If I start multiplying out everything to get the LCD my final answer will be huge. Thanks in advance
 
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It shouldn't be too terrible. The obvious thing to note is that (b - a) = -(a - b), for example.
 
Write everything with a denominator of (a-b)(a-c)(b-c) and add the fractions.
 
basic advice: do not fear to write something down, just because you think it will be large and unmanageable. you have to plunge in without fear of what will come out. you have to get your hands dirty.
 

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