Note that this limit only exists from the right.....
lim x -> 0+ x-sqrt(x) / x + sqrt(X) multiply both by x - sqrt x on top and bottom
lim x -> 0+ [x^2 - 2xsqrt(x) + x] / [x^2 -x] factor x out of top/bottom
lim x -> 0+ [x - 2sqrt(x) + 1] / [x - 1] let the limit go to 0
= -1
Here's the graph : https://www.desmos.com/calculator/gnp5cfkzde