Originally Posted by

**Sneaky** i got to the step

-3x (1/-x)

-------------------------

(x- sqrt(x^2 + 3x))(1/-x)

then for the numerator i simplify and get 3

but for the bottum part i dont see how you get -2

and why does 3/x = 0, why do you assume that?

Oh, dear god: who ever wrote such a nonsense?! I said 3/x --> 0, not equality! Meaning, of course, that x--> oo or x --> -oo, it's the same in both cases.

Now the denominator:

(x- sqrt(x^2 + 3x))(1/-x) = x*(-1/x) - (-1/x)Sqrt(x^2 + 3x) =

-1 - Sqrt([x^2 + 3x]/x^2) = -1 - Sqrt(1 + 3/x)

Rememebr that if a is a non-negative real number, the a*Sqrt(h) = Sqrt(ah) , and this is why we needed -1/x = 1/-x and NOT 1/x, because since

we're taking the limit as x --> -oo we're going to work with NEGATIVE x's, so in order to get somethinbg into a square root we took -1/x, which is POSITIVE (as 1/x is negative!).

Tonio

Pd. Read carefully this and my prior answers, work on them with pencil and paper, THINK...and after a good while of honest effort, if you don't succeed then write back.

why does

-sqrt(x^2 + 3x)

---------------- = -1 ?

-x