FDP Guide Pg. 37 #7

[BK87]

Question:

Simplify: 8(3)(x)^2(3) over 6x

The solution according to the guide is 12x. My question is, why is the answer not 12x^2 over x? No where in the problem does it say that x does not equal zero. How come we are allowed to cancel out the x in the dominator?

Thanks.

[tim]

Any time you see a variable in the denominator, that is an implicit guarantee that the variable cannot be 0. Remember, you cannot divide by 0, so if you see the GMAT dividing by a variable, it is not 0.

[RonPurewal]

at the beginning of every official GMAT (and in the introduction to the math chapters in the OG), you'll see this specification: "All numbers are real numbers."

ordinarily, there will also be prohibitions that prevent this sort of thing from happening anyway. (e.g., if a denominator is x(x – 1), then the problem will specify that x ≠ 0 and x ≠ 1.) but, even if those prohibitions are absent, "all numbers are real numbers" still guarantees that you won't divide by zero.