Let's first look at a simpler equation more likely to resemble what you'd see on the GMAT:

ab = a

You cannot just divide by a on both sides here and conclude that b=1, because it might be true that a=0, and you can never divide by 0. If you want to solve this equation by dividing by a, you must divide the problem into two cases:

1. either a=0 (quickly check if that could be true, and it can)

or

2. a is not 0, and we can divide by a on both sides, so b=1

So the equation ab=a means one of two things must be true: a=0, or b=1 (or they could both be true).

I'd never solve an equation like ab=a in that way, however. It's less confusing just to get 0 on one side and factor:

ab = a
ab - a = 0
a(b-1) = 0

so a=0 or b=1 (or both).

In your solution:

minihobel wrote:
Please have a look at no. 2. above...I'll solve differently
2. x^2(x-1) - 9(x-1) = 0
3. x^2(x-1) = 9(x-1)
4. x^2 = 9
Solution x = 3 or -3 (doesn't matter to answer the question) => (1) IS sufficient

going from step 3 to step 4, you divided on both sides by x-1. You can't do that, because x-1 might equal 0. So you lost one of the solutions for x in that step. You don't run the risk of losing solutions in that way if you always factor equations like this.

you might be interested in this article called "Can You Divide by Variables?" https://www.gmatprepnow.com/articles/can ... -variables

Cheers,
Brent