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:
$ab + a = 1$ (for a)

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

$a = (1-a)/b$ (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?

$a = 1/(b+1)$

2. Originally Posted by piercedgeek
$ab + a = 1$ (for a)
a(b + 1) = 1
a = 1 / (b + 1)

3. ok, after reviewing some old examples, I see I can use the distributive property
to re-write ab+a as a(1+b), so,
$a(1+b) = 1$ (divide by 1+b)

$a = 1/(1+b)$

and it's done...

But I think this is the source of a lot of the problems I have with questions that have multiple variables.
The book would describe this as "using the distributive property to write the sum of ab+a as a product of a and 1+b"
But for some reason I just have a hard time seeing this particular method in my head, so I freeze when a problem requires it... Does anyone have another way to view this?

4. Sorry to be almost talking to myself on this forum, I've been staring at this problem for longer than I care to admit, with no progress, and after talking/typing things out, the gears are starting to turn in my head. It just hit me, and I figured I'd share in case anyone else is having a brain fart moment like myself:
a+ab can be written as a(1+b) because a(1+b) can be distributed to a+ab

could be time for bed