Have you ever heard of L Hopital's rule? Basically if you have a limit of a ratio you can take the derivative of the top and bottom pieces separately and it it will still result in the same limit.

For your first one you have:

derivative of top: 1/2*(x-2)^(-1/2) + 1/2*(6-x)^(-1/2)
derivative of bottom: 1

limit x->3 = 1/2*(3-2)^(-1/2) + 1/2*(6-3)^(-1/2)
= 1/2*(1) + 1/2*(1/sqrt(3))
= 1/2 + 1/(2*sqrt(3))

I'm not going to do the second one because it's your homework, and math is a bitch to type out.