Simplification

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/