I'm a little embarrassed, this question looks so simple, but I'm obviously forgetting something basic when trying to solve it, because I end up not making it to the final answer in the book.

Question:

$\displaystyle ab + a = 1$ (for a)

$\displaystyle ab = 1 - a$ (minus a from both sides)

$\displaystyle a = (1-a)/b$ (divide by b)

I know this isn't the final answer, because we still have a on both sides, but I just feel stuck. I know I can make it 1/b - a/b, but can't remember how to get rid of the a. Did I forget something simple here? or do something incorrect earlier that has painted me in to an impossible corner?

Book answer:

$\displaystyle a = 1/(b+1)$