I'm thinking this is what the problem looks like: [tex] \frac{4}{x-4}= \frac{x}{x-4}- \frac{4}{3} [/tex]. The first thing to do is to move the [tex] \frac{x}{x-4} [/tex] over to the other side because it has a common denominator with the other side. Doing that and at the same time combining them over their common denominator looks like this: [tex] \frac{4-x}{x-4}= -\frac{4}{3} [/tex]. The best way to solve for x now is to cross-multiply to get 3(4-x)=-4(x-4). Distributing through the parenthesis is 12 - 3x = -4x + 16. Solving for x gives us x = 4. Of course when we sub a 4 back in for x we get real problems, don't we? Dividing by zero breaks every rule in math that there ever was! So, yes, the solution is extraneous.
