When you divide by an algebraic expression (like x-1), there's a chance that you are dividing by zero.
If you divide by zero, the resulting equation may be meaningless.
For example, we know that (2)(0) = (1)(0)
If we divide both sides by zero, we can't conclude that 2 = 1

The same applies to x^2(x-1) = 9(x-1)
If we divide both sides by (x-1), we can't conclude that x^2 = 9

Cheers,
Brent

Hi Amrabdelnaby,

You have to be VERY careful when you divide by a variable. By doing so, you might end up 'losing' one of the solutions to the original equation/question.

Here's a simple example:

X^2 = X

Mathematically, this equation has 2 solutions: 0 and 1. You can prove that by doing the following....

X^2 = X
X^2 - X = 0
X(X-1) = 0

X = 0, 1

However, if you chose to divide both sides by X to start, you'd have.....

X^2 = X
X = 1

By dividing, you "lost" the solution X=0.

These types of 'tests' often show up in DS questions (since DS questions test the 'thoroughness' of your thinking, among other things). Thus, it's important to be careful about how you choose to do your math - the scope of the correct answer depends on it.

GMAT assassins aren't born, they're made,
Rich