I have this algebraic fraction sum I need help with.

I worked it out by cancelling out the x^2 on both sides, and then simplifing the rest, and my answer was:Code:x^2 - 7x ------- x^2 - 49

I read that the correct method would be this:Code:x -- 7

Why is this right, and my method wrong? My reasoning is that the denominators are the same for x^2 and 7x, so I can just work by simplifying them...Code:x(x-7) x --------- = ---- (x+7)(x-7) x-7