Algebra problem

[straightflush]

I was sitting in a computer lab and I saw this writen on a blackboard...

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

I'm smart enough to know the error is on the left side of the equation. I'm just having trouble figuring out why you can't do this (other than the obvious x - x = 0).

Obviously it's been too long since I took algebra so don't be too hard on me. A quick explaination why this is not valid would be appreciated.

[oneeye13]

look at the other thread titles for your answer

[Copernicus]

so why are you discounting the obvious as being the problem?

[VickreyAuction]

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look at the other thread titles for your answer

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[straightflush]

[ QUOTE ]
look at the other thread titles for your answer

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I don't get it. Are you telling me there is a similar post that has been made recently?

[oneeye13]

[ QUOTE ]
[ QUOTE ]
look at the other thread titles for your answer

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I don't get it. Are you telling me there is a similar post that has been made recently?

[/ QUOTE ]

look at the titles of spoohunter's recent posts

also, ask yourself which is the last correct line

[straightflush]

Ok, makes sense.

Somehow I was hoping for a better explaination than, "division by zero." I guess this is why I'm not a math major.

[oneeye13]

[ QUOTE ]
Ok, makes sense.

Somehow I was hoping for a better explaination than, "division by zero." I guess this is why I'm not a math major.

[/ QUOTE ]

well, this derivation is basically:

0*1 = 0*2
therefore, 1=2

but, by using (x-x) instead of zero, they've obscured it a little

[straightflush]

Thanks, sorry for wasting everyones time. Those x's can be tricky.

[tilted]

x^2 - x^2 doesnt not factor to (x + x) * (x - x)

[chief444]

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

But you obviously can't divide by (x-x).

[tilted]

(x+x)*(x-x) = (x+x)*0 = 0

[Fly]

[ QUOTE ]
x^2 - x^2 doesnt not factor to (x + x) * (x - x)

[/ QUOTE ]

It doesn't matter if it factors into that or not since both quantities are equal to zero and thus equal to each other. The only problem is division by zero.

[Copernicus]

[ QUOTE ]
(x+x)*(x-x) = (x+x)*0 = 0

[/ QUOTE ]

You are reducing before multiplying, that doesnt mean that the product cant be factored back to its multiplicands.

(9x^2-36) certainly factors to (3x-6) * (3x + 6), however when x=2 that is 0 * (3x +6) = 0, or it is (3x-6) * 12. You cant return to the original form from either one without knowing the interim step before reduction.

[chief444]

[ QUOTE ]
(x+x)*(x-x) = (x+x)*0 = 0

[/ QUOTE ]
= x^2-x^2

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