You have to be careful when dividing by variables because you might accidentally REMOVE a potential solution to the equation.
Here's a simple example of that 'error':
How many solutions does the following equation have?
X^3 = X
Without too much trouble, you should realize that the solutions are...
If you divide both sides by X though, you get....
X^2 = 1
Now the solutions are....
-1 and 1. WHERE did the 0 go????? You divided it "out" when you divided both sides by X
Since each prompt requires that you properly deal with what you were given, you are responsible to find ALL of the potential answers. If you're thinking about dividing by a variable, then you might instead try factoring the equation first.
GMAT assassins aren't born, they're made,
EMPOWERgmat GMAT Club Page, Study Plans, & Discounts