Algebraic expressions - simplifying

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SUMMARY

The discussion focuses on simplifying the algebraic expression 1/(a-b)(a-c) + 1/(c-a)(c-b) + 1/(b-a)(b-c). Participants emphasize the importance of finding a common denominator, specifically (a-b)(a-c)(b-c), to combine the fractions effectively. They advise against hesitance in manipulating the expression, as the process may initially seem daunting but is essential for arriving at a simplified result. The key takeaway is to embrace the complexity of the calculations to achieve clarity in the final expression.

PREREQUISITES
  • Understanding of algebraic fractions
  • Knowledge of finding common denominators
  • Familiarity with the properties of algebraic expressions
  • Basic skills in manipulating algebraic equations
NEXT STEPS
  • Practice simplifying complex algebraic fractions
  • Learn about common denominators in algebra
  • Explore techniques for manipulating algebraic expressions
  • Study the properties of rational functions
USEFUL FOR

Students preparing for standardized tests like the GRE, educators teaching algebra, and anyone looking to improve their skills in simplifying algebraic expressions.

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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