Rearranging the equation to make x the subject

Hello, I have a question that I need to rearrange to make x the subject.

a(x-b)=x+c

I tried various ways to make x the subject but I always find that x cancels itself, but I know there is definitely a way to express x without it cancelling out.

If someone can explain this step by step that will be great.

Re: Rearranging the equation to make x the subject

$\displaystyle ax - ab = x + c$. Move all terms with "x" to one side, and all the constants to the other side.

$\displaystyle ax - x = ab + c$

$\displaystyle x(a - 1) = ab + c$

$\displaystyle x = \frac{ab + c}{a - 1}$