Factor and Simplify
Date: 4/10/96 at 21:41:35 From: Anonymous Subject: Complex Fractions How would you do the following problem and if possible, please give tips for how to do similar problems. Thank you for the help. (1/x^2-1/y^2)/(1/x^2+2/xy+1/y^2) Factor whenever possible.
Date: 5/28/96 at 20:33:24 From: Doctor Pete Subject: Re: Complex Fractions Let a=1/x, b=1/y. Then your expression is equivalent to (a^2-b^2)/(a^2+2ab+b^2) which you can factor as (a+b)(a-b)/(a+b)^2, so this is (a-b)/(a+b). Substituting back, we get (1/x-1/y)/(1/x+1/y) = ((y-x)/xy)/((x+y)/xy), so your expression is equal to (y-x)/(x+y). The trick in this case was to look at your x's and y's, and notice that they were all reciprocals, so you can do a substitution that makes the factorization much easier to spot. Here's one in a similar vein, but a bit trickier: Simplify (x-y)/(sqrt(x)-sqrt(y)) . -Doctor Pete, The Math Forum
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