OT: Any Math people in here?

I hope to teach this crap to kids someday so I figured I give this problem a try.

I think all we want to do is pull out common factors and reduce the fraction so the terms in the top part...

8*a^2*m - 32*b^2*m

have 8 and m in common. We can pull those out to rewrite it as...

(a^2 - 4*b^2)*(8*m)

The terms have nothing else in common so that's it for the top. Now for the bottom...

4*a*x + 8*b*x

Okay so in the bottom part we can see that the terms have 4 and x in common (4 and x are multiplied with both a and 2*b) so let's pull those out.

(a + 2*b)*(4*x)

So our fraction (it's not an equation because they haven't given us an = sign) becomes...

(a^2 - 4*b^2)*(8*m)
---------------------
(a + 2*b)*(4*x)

This is where the crappy part comes in. If you look at the terms on top and on bottom there is something they have in common (we can divide things into other things). It's real easy to see that we can divide 8 by 4 to get...


(a^2 - 4*b^2)*(2*m)
---------------------
(a + 2*b)*x

But we can also do something with (a + 2*b). It will divide into (a^2 - 4*b^2) if we factor (rewrite) the top into (a + 2*b)*(a-2*b). If you use "foil" on it you'll see that...

(a + 2*b)*(a - 2*b) becomes a^2 + 2*a*b - 2*a*b - 4*b^2 which is a^2 - 4*b^2

That's the crappy part, not so much the foil thing, but seeing that (a^2 - 4*b^2) can be factored.

Okay so now if we factor and rewrite our fraction we see...

[(a + 2*b)*(a - 2*b)]*(2*m)
----------------------------
(a + 2*b)*x

So you can see that the (a + 2*b) can divide into the top, I like to say that it cancels out since it is on both top and bottom. and our fraction becomes...

(a - 2*b)*(2*m)
----------------
x

Smooth huh? No it sucks I'm not going to lie to you, but it's math and it is an important tool that can be used to solve a lot of problems (like figuring out how far you can go on a tank of gas, or your suspension geometry). Learn it and you be ahead of so many others that can't do it. A TI 89 will solve these type problems symbolically. It is an awesome tool that really helps with the algebra crap. Don't go to engineering school without it.

That help?