
Re: simplifying rational expressions
Posted:
Jan 16, 2013 3:34 AM


stony writes:
> 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? > > My daughter was trying to solve this, but ended up with the mess and > then I got the same mess, but I thought there may be an easy way to > simplify this that I may be missing. > > ((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.
I suspect you are missing the fact that (a  b) and (b  a) in the denominators are essentially the same factor. The common denominator of the terms is (a  b)(a  c)(b  c). I think you can leave the denominator in that form.
I did the numerator two ways: in terms of these same factors, and multiplying out and combining terms. They seemed about equally simple to me, though I may have made mistakes. I usually do. Be careful with the signs :)
Hope this helps.

