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more algebra assistance

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more algebra assistance [#permalink] New post 12 Jan 2013, 18:02
if ((y+4)(y-4)) / 3x is equal to (y-4) / 6 and you know that y does not equal 4, then how do you know to simplify the formula to (y+4) / 3x = 1/6 ????
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Re: more algebra assistance [#permalink] New post 12 Jan 2013, 18:13
Divide both sides by (y-4)!
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Re: more algebra assistance [#permalink] New post 12 Jan 2013, 18:17
PraPon wrote:
Divide both sides by (y-4)!


i understand that but why does MGMAT preface with "since y does not equal 4"? I guess I was confused as to why that is relevant to simplifying?
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Re: more algebra assistance [#permalink] New post 12 Jan 2013, 19:03
IF y=4 then y-4=0. You cannot divide both sides by 0. As the question says Y is not equal to 4, you can safely take out (y-4) from both sides.
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Re: more algebra assistance [#permalink] New post 15 Jan 2013, 05:22
Expert's post
jmuduke08 wrote:
if ((y+4)(y-4)) / 3x is equal to (y-4) / 6 and you know that y does not equal 4, then how do you know to simplify the formula to (y+4) / 3x = 1/6 ????


Division by 0 is not allowed. It gives an undefined value. So you cannot divide both sides of an equation by a variable until and unless you know that the variable is not 0.

e.g. Given
x = x^2
Here, you cannot say that x = 1 if you are not given that x is not 0. This is because you cannot divide both sides by x since x can be 0. To handle this, you need to do the following:

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

Either x = 0 or x = 1

If you had known that x is not 0, you needn't do all this. Then you can simply divide both sides of the equation by x and get x = 1.

The same concept is used here as explained by PraPon.
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Re: more algebra assistance   [#permalink] 15 Jan 2013, 05:22
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