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:
Write as a single fraction.$$-\frac{3b-5y}{2b} + \frac{3b+6y}{8b} + 2$$Simplify your answer as much as possible.
And this is what we got...$$\frac{7b+26y}{8b}.$$
It's just like adding fractions; find a common denominator and add. Here $8b$ is a common denominator. We get $$ -\frac{4}{4}\frac{3b-5y}{2b}+\frac{3b+6y}{8b}+\frac{8b}{8b}\frac{2}{1} $$ $$ =\frac{-4(3b-5y)+(3b+6y)+8b(2)}{8b} $$ $$ =\frac{-12b+20y+3b+6y+16b}{8b} $$ $$ =\frac{7b+26y}{8b} $$