Question

How do you simplify `(ax - ay - 2by + 2bx)/(ax - 2bx + 2by + ay)`?

Answer 1

`=>(x-y)/(((a-2b)/(a+2b))x+y)`

Explanation:

I don't think this can be simplified much:

`=>(ax - ay - 2by + 2bx)/(ax - 2bx + 2by + ay)`

I tried the following. I combined coefficients:

`=>((a+2b)x-(a+2b)y)/((a-2b)x+(a+2b)y)`

Then I saw that three out of four terms contained the same coefficient. So I divided by it:

`=>(x-y)/(((a-2b)/(a+2b))x+y)`

I guess this is a little better than the original, because whatever `a` and `b` happen to be, they only influence the one term in the denominator and it's easy to see how with this form.