Date: 05/04/97 at 14:04:14 From: Ong Keng Guan Subject: Algebraic Terms For one of my algebra questions, I was asked to simplify a complicated expression and I obtained (1/a) + (1/b). I then had an argument with my friend who insisted that it is not fully simplified until I convert it into a single term: (a+b)/ab. What do you think? Gratefully yours.
Date: 05/05/97 at 14:27:36 From: Doctor Ceeks Subject: Re: Algebraic Terms Hi, The form in which you ultimately choose to express a formula often depends on what aspect of the formula you wish to bring out. The choice of what aspect to emphasize is often dictated by what problem you wish to solve. In the absence of such factors, however, simplification becomes subjective. My personal feeling, in the absence of such factors, would be to leave it as you have it: 1/a + 1/b. However, as an example to make more concrete what I'm talking about, suppose this problem came from the following situation: The roots of x^2-Sx+P are a and b. Suppose you are told S and P, but not a and b, and you want to determine some formula which simplifies to 1/a + 1/b. In this case, I might prefer to reexpress the result as (a+b)/(ab), as your friend did, because if a and b are the roots of that quadratic, then a+b = S and ab = P. Expressing the formula as your friend did then makes it clear that the formula is really S/P, and since we're pretending that it is S and P that you are actually given, this formula is more directly applicable to the problem. -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.