absolute value

[mariah]

If x is nonzero, |x^2|/x=?
I. x
II. |x|
III. x^2/x

oa [spoiler]1&3[/spoiler] why not II?

[cramya]

Take x to be some negative value
If x is -2 then |x^2| /x = -2 which is x and not |x|

Hence II is not possible.

[mariah]

i must get some sleep )

[lunarpower]

cramya has it nailed.

here's the more general takeaway: make sure you know which number types are associated with which operations.
in this particular case, this means that you should see the absolute value, and make an instant connection with positive/negative/zero.

the other takeaway is that, if at all possible, you should immediately start plugging in numbers if you aren't 100% sure of the theoretical approach to a problem.

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finally, note that |x^2| is actually the same as just x^2, since x^2 can't be negative. therefore, this problem is merely asking you to divide x^2 by x, producing x.