Simplify the expression, where x is negative

Simply

f(x) = (sqrt((x^4)+3x^2)) / x

where x is negative.

I get sqrt((x^2)+3) but the seems to be the wrong answer

f(x) = (sqrt((x^4)+3x^2)) / x

f(x) = (sqrt[x^2((x^2) + 3)]) / x

f(x) = |x| (sqrt(x^2 + 3)) / x

since x is negative, to get rid of | x |, you need to add a "-"; negative sign in front of it.
So, the function becomes

f(x) = (-x) (sqrt(x^2 + 3)) / x

f(x) = -sqrt(x^2 + 3)

If I take the positive root of x^2 when simplifying the radical, dividing it by the negative x in the denominator will give me negative sqrt(x^2 + 3).