I get -.5, but you need to be careful with the negative sign.
Moving an x through a square root is not x, but |x|=-x in this case.
let w=-x and then multiply top and bottom by the conjugate and see what you get.
as x approaches negative infinity, what value does this function approach ?
limit square root (X^2+X) + X
i manipulated it to take out absolute (x) from the square root
so, limit absolute value (x) square root (1+1/x) +x
now, i get infinity - infinity.
I do not know where to go from this point.