Question

Lim x>0 (sqr5+x-sqr5)/x

Answer 1

First step in evaluating limits:
simplify the algebra and see what you get.
If you get:
(a number), then it is also the limit.
(∞/(a number)), the limit is &infin.
(0/(a number)), the limit is 0.
(∞/∞), or (0/0), then you need other techniques/tools.

Try the first step shown above and tell us what you get.

Answer 2

some parentheses would also help.

Since (√5 + x - √5)/x = 1, that's probably not what you had in mind.

(√(5+x)-√5)/x -> 0/0

so, multiply top and bottom by (√(5+x)+√5) and you end up with

((5+x)-5)/(x(√(5+x)+√5))

see where that takes you...