Calculate limit of this expression

I'm trying to solve this problem from Demidovich's book, but I only managed to confuse myself:

206.

lim x --> 4

[ 3 - root(5+x) ] / [ 1 - root(5-x) ]

I'd appreciate any help.

Since this evaluates to 0/0 at x=4, you can use l'Hopital's rule.

lim (x->4) [ 3 - root(5+x) ] / [ 1 - root(5-x) ]
= lim (x->4) [d/dx (3-sqrt(5+x))] / [d/dx (1-sqrt(5-x))]
= lim (x->4) [-1/(2sqrt(5+x))] / [-1/(-2sqrt(5-x))]
= lim (x->4) [(-2sqrt(5-x))] / (2sqrt(5+x))
= -1/3

The answer is -1/3.

Simple, the limit does not exist.