Why Did the Negative Sign Disappear in the Calculus Example?

[kLPantera]

http://math.colorado.edu/~jkeller/math1300/lectures/L8limits3.pdf

Example 8, the 2nd to 3rd step... where did the negative go? It's (x^2 - 3x) - x^2 then it became 3x in the numerator. Where'd the negative go? I don't see any other sign changes so could someone please tell me?

 

[Ray Vickson]

It looks like an error: the minus sign should not have gone away. Intuitively, you can see the answer must be <= 0 because sqrt(x^2 - 3x) < x for x > 0, so when we subtract x we get a negative result. That does not allow for a positive limit.

RGV