Can anyone help me with this limit problem

How do you find the limit as x approaches 0, of x/((√x+1)-1)?
Could you show how you solve this problem?

lim x/(√x+1 -1)
x->0

lim x(√x+1 +1)/(√x+1 -1)(√x+1 +1)
x->0

lim x(√x+1 +1)/(x+1-1)
x->0

lim x(√x+1 +1)/x
x->0

lim √x+1 +1
x->0

as the limit approaches 0 then

√0+1 +1 = 2

the limit is 2

x/((√x+1)-1)

Multiply the top and bottom by (√(x+1) + 1) to rationalize.

x/((√x+1)-1) * (√(x+1) + 1)/(√(x+1) + 1)

x(√(x+1) + 1) / (x+1-1)

x(√(x+1) + 1)/x

√(x+1) + 1

Now you can plug it in.
√(x+1) + 1
√(0+1) + 1
√1 + 1 = 2

*sigh*
whats the problem???
use l'Hospital's rule.
it is trivial.
and doesn't require a bunch of algebra.