How do I find the limit of --> lim (as x approaches 1) of ((x^-0.5)-1)/(x-1)

can you help me please? I need to know the steps because I dont know how to do it :/

help is appreciated :)

x^-0.5 can be written as 1/x^0.5

so we hav

lim(x--->1) ((1/rootx)-1)/x-1
multiply numerator and denominator with rootx
=lim(x--->1) (1-rootx)/[(rootx)(x-1)
multiply this function with 1+rootx/1+root x
note that (1-rootx) (1+rootx) = 1-x
=lim(x--->1) 1-x/[rootx(x-1)(1+rootx)]
x-1 is common in numerator and denominator

so you get
lim(x--->1) (-1)/(rootx(1+rootx))
substitute x=1

=-1/2