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Re: simplifying rational expressions
Posted:
Jan 16, 2013 3:49 AM


On Tue, 15 Jan 2013, stony wrote: > > Need a little help with this. We are simplifying the following, but > the solution is pretty lengthy and messy because of the enormous > number of factors. I was thinking that may be I am missing seeing a > pattern (some series or something). Is grunt work the only way to > solve this or is there a pattern that can simplify the whole process? > Write very neatly and work methodically cheching and doubling cheching each step as you go and again afterwards.
> ((bc)/((ab)(ac))) + ((ca)/((bc)(ba))) + ((ab)/((ca)(cb))) + > (2/(ba))  (2/(ca)) > > of course, I took all the factors in the denominator and then started > multiplying the numerator with the remaining factors to end up with a > mess.
(bc)/((ab)(c  a))  (ca)/((bc)(a  b)))  (ab)/((ca)(b  c)))  2/(a  b)  2/(ca)
[(b  c)^2 + (c  a)^2 + (a  b)^2 + 2(b  c)(c  a) + 2(a  b)(c  a)]
[b^2  2bc + c^2 + c^2  2ac + a^2 + a^2  2ab + b^2 + 2(bc  c^2 + ab + ac) + 2(ac  bc  a^2 + ab)]
[b^2  2bc + 2ab + 2ac]



