# Simplifying a Multi-Variate Fraction

I am an eighth grader in need of a little assistence. I was given a multi-variate fraction, and was told to simplfy it to lowest terms. On of my fellow classmates that is ahead of me in math, tried to explain it to me, but he didn't make sense. We ended up with an answer (shown below), but I wasn't sure how we got it. I want to know this because I feel that it might be important when I embark on Geometry next week. Any ideas?

This is the problem:

And this is what we got...

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You know how to take the LCM, yes? –  Ｊ. Ｍ. Feb 3 '12 at 15:56
Wait! Least Common Multiple? If that is correct, then yes –  CodeAdmiral Feb 3 '12 at 16:00
You've got the correct answer, so you may know how to combine fractions just fine. For us to make sure, write out all the working that goes through your head step by step. –  Ragib Zaman Feb 3 '12 at 16:02
As an answer? I can so that in like half an hour... I have reading time now –  CodeAdmiral Feb 3 '12 at 16:05
it's just like adding fractions; find a common denominator and add. here $8b$ is a common denominator. we get $$-\frac{4}{4}\frac{3b-5y}{2b}+\frac{3b+6y}{8b}+\frac{8b}{8b}\frac{2}{1}$$ $$=\frac{-4(3b-5y)+(3b+6y)+8b(2)}{8b}$$ $$=\frac{-12b+20y+3b+6y+16b}{8b}$$ $$=\frac{7b+26y}{8b}$$