When can I be confident that I can cancel out variables?

Question

I think I am confused as to when I can cancel out variables.

For example,

3w^2 = 6w
3w = 6
w=2

I'm aware that cancelling w's on both sides make me lose of the x solutions, so I should not cancel out w.

Now if we look here ,

x^2 - y^2 = x - y
(x+y)(x-y) = (x-y)

{(x+y)(x-y)}/(x-y) = (x-y)/(x-y)

(x+y) = 1

This is valid.
However, when I'm thinking inside my head, I feel hesitant to perform cancellations like that because I am scared I might lose possible actual answers like the one I mentioned above. This makes me scared, panic and make me lose time.

Any definite approach and proper concept that could help me think straight and confident regarding this situation?

Thanks,

WoundedTiger · Answer

Hi uwengdori, I will try and answer your question. The variables are generally cancelled when they are of same sign. Case 1 :3w^2 = 6w In Gmat, It is not wise to cancel out and for the above you can do it as below 3w^2- 6w = 0 3W (W-3)=0--------> 3W=0 or W=0 or W=3....So there are 2 solutions to this question In the second question x^2-y^2= x-y....Let us follow the same method Taking (x-y) common we get ----> (x-y){x+y-1} =0 or x=y or x+y=1 For more on these, please refer to Math club chapters on Algebra... The link is algebra-101576.html#p787276 Happy Gmating!!!!

DDB1981 · Answer

when you get an equation like 3w^2 = 6w, you might be tempted to cancel the w's, and it's perfectly cool to do so, but remember WHAT cancelling means:

when you cancel the w's here what you are implicitly doing is DIVIDING BOTH SIDES BY "w"

seems harmless cuz there's a W on each side right? except for one thing, if the W happens to be zero, you're dividing by 0, which is one of math's cardinal sins!

so when you do this operation, keep in mind the fact that W might actually also be 0 (which you can easily test: plug in 0 into W, and if the equation works, the 0 is at least one of the answers). If this is the case, you can still simplify, but you need to keep the case where w=0 in your back pocket in case you need to use it, and if you don't need to use it, no harm done: your equation is simplified

hope this helps, but don't be shy if it doesn't!

KarishmaB · Answer

To make the decision easier for you - never cancel out the variables. 
You may be able to cancel it out depending on what is given or not given in the question but if you do not cancel it, you will not be wrong.

3w^2 = 6w
3w(w - 2) = 0
w = 0 or 2

Now if we look here ,

x^2 - y^2 = x - y
(x+y)(x-y) = (x-y)

(x + y)(x - y) - (x - y) = 0
(x - y)(x + y -1) = 0
x - y = 0 or x+y = 1
So either x = y or x+y = 1
If it is given to you that x is not equal to y, you ignore the first solution and go with the second.

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When can I be confident that I can cancel out variables?

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