What am I doing wrong in this limit calculation?

Hello everyone,

I have tried to calculate the following limit of a function, but my result doesn't match the one that my computer gives me.

First I multiply by , which gives me

Next I simplify the numerator and factor x out of the roots in the denominator

x cancels out, which gives me

My computer algebra system however tells me that the limit is 1/2. It would be -1/2 if x were approaching positive infinity, so I my problem is somehow related to x approaching negative infinity. But what exactly is it that I am doing wrong?