There may be an easy way to solve this, but I do not see it.
First, graph the expression for which the limit is required. You should see that the values near 3 are negative and near -0.05.
Second, get expressions for the fraction when x=3+h and x=3-h and show that these expressions are equal and negative near h=0 with value near -0.05.
Third, write Taylor series expansions for the radicals in the numerator obtained in the 2nd step above. Show that the numerator is -h/6 when higher order terms are ignored. If higher order terms in the denominator are ignored, the denominator is 3h. The limit then is -1/18 which is approximately -0.055.
I am not sure that the procedure in the 3rd step is valid, but the numerical values obtained suggest that it is.
If you get a better answer from another tutor or if you get a better answer in class when you review this problem, I would certainly appreciate some feed back.