Where is the error in this basic factoring problem?

[quicknote]

I know this must be a basic factoring question but I don't get it. Somewhere in the solution below there is an error which leads to an end result of 1 = 2. I'm supposed to find where the error lies.

The factoring looks right. I think the error is in line three. you can only multiply or divide a factor (common factor between both sides) and can't subtract... am I on the right track or just grasping at straws?

Thanks for any help

x = x
x^2 = x^2
x^2 − x^2 = x^2 − x^2
x(x − x) = (x + x)(x − x)
x = (x + x)
x = 2x
If we let x =1, then upon substitution we have
(1) = 2(1)
1 = 2

 

[Moo Of Doom]

ab=ac implies b=c only if a does not equal 0. So you can't get from x(x-x) = (x+x)(x-x) to x = (x+x) since (x-x)=0. You're effectively "dividing by zero" in that step. This is one of the many reasons division by zero isn't allowed.

 

[shmoe]

Line 3 is fine.

Maybe try substituting x=1 in each line. You should be able to spot which line contains the first error, then look at the last operation you did carefully.