...what?

It actually means "Is defined to be".

You might of given us something wrong, which is why we keep getting x - 6 = x + 6. I'm guessing the left side is supposed to be x - 6, not x + 6.

If everything is correct then then the left is not defined to be the right. My proof:

Quote from name:Shocko

((x - 3) / x) - ((x - 2) / (x+2)) = ((x + 6) / (x (x +2)))

Ugh, too many unnecessary parenthesis!

(x - 3) / x - (x - 2) / (x+2) = (x + 6) / (x (x +2))
(x+2)(x-3) - x(x-2) = x+6
x²-x-6-x²+2x = x+6
x-6 = x+6.

Wait, if it means that it "is defined to be" we cannot treat it like an equation. YAY my bitch of a math teacher pulled through! We learned this with trigonometric functions, and proving them equal to other trig functions with some stuffs attached. We have to take one side, and use different stuffs, to prove that the side we started with is equal to the other side. I'll start on the left.

(x - 3) / x - (x - 2) / (x+2) = (x + 6) / (x (x +2))
(x-3)/x - (x-2)/(x+2)
(x+2)(x-3)/x(x+2)-x(x-2)/x(x+2)
(x+2)(x-3)-x(x-2)/x(x+2)
(x²-x-6-x²+2x)/x(x+2)
(x-6)/x(x+2)

Yeah, I'm starting to think it should be x-6 not x+6 on the right half, there bro. It's a lot harder to mess up with just plain numbers and variables than it is when you have to remember 30-odd properties of sines, cosines, tangents, cosecants, secants, and cotangents.

EDIT: o hai, someone posted a better looking model, and I didn't think anyone would've thought back this far to remember this proof crap.

Let's have a math challenge every week.

I second this motion! Lets do calculus!

((x - 3) / x) - ((x - 2) / (x+2)) = ((x + 6) / (x (x +2)))

x-3 x-2 x+6 x != -2 and 0
---- - ----- = -----
x x+2 x(x+2)

(x+2)(x-3) - x(x-2) x+6
----------------------- = -----
x(x+2) x(x+2)
x^2-3x+2x-6 - x^2+2x x+6
--------------------------- = ------
x(x+2) x(x+2)
x-6 x+6
------- = ------
x(x+2) x(x+2)

x-6 = x+6
-6 = 6
There is no solution? Oo

Edit: I'm quite certain that if we wanted to get a solution, it should be either (x+3) in the 1st one of (x+2) in the second one...

There can't be no solution because it isn't an equation to begin with. All that can be said is that the left expression is not defined to be the right lol.

@ math contest: No fuck you.

Lawl. I'll take that as a yes.

I tried that in the Null a long time ago. It died out.

Let's do it again. I'll win.

I third this notion... But make it Applied Physics.

Quote from Generalpie

Quote from MasterJohnny

Quote from BeDazed

Let's have a math challenge every week.

I second this motion! Lets do calculus!

I third this notion... But make it Applied Physics.

I (quarter? fourth?) this motion...But make it raping.