Hi, I've been away from math for a few years now and coming back to it with an algebra review I've run into a problem.

I was answering a question:

Solve the equation $\displaystyle \dfrac{x}{6x-36} -7 = \dfrac{1}{x-6}$

I ended up with x = 6 , inputting that into the system gave me a "wrong answer". I noticed that plugging x=6 into the original equation causes a couple of divisions by zero so I inputted the answer as "none", that came back as correct.

Great, I got it correct! Problem is I don't really know WHY. For one I don't know why I had to plug the x=6 back into the equation to get my answer. And secondly the only reason I understand this as having "no answer" is because I saw the big scary divide by zero's come up.

I'm pretty sure I knew why I had to do these things back in high school! Too bad I can't remember now

Can anyone help me out with this? Let me know if this doesn't make any sense heh.