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

Mar 27, 2018

$\implies \frac{x - y}{\left(\frac{a - 2 b}{a + 2 b}\right) x + y}$

#### Explanation:

I don't think this can be simplified much:

$\implies \frac{a x - a y - 2 b y + 2 b x}{a x - 2 b x + 2 b y + a y}$

I tried the following. I combined coefficients:

$\implies \frac{\left(a + 2 b\right) x - \left(a + 2 b\right) y}{\left(a - 2 b\right) x + \left(a + 2 b\right) y}$

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

$\implies \frac{x - y}{\left(\frac{a - 2 b}{a + 2 b}\right) x + y}$

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.