Question

limit x tends to infinity ( 1+root n)/(1-rootn)

Answer 1

You must have meant:
lim (1 + √n)/(1-√n) as n ---->∞
divide top and bottom my √n
= lim (1/√n + 1)/(1/√n - 1) as n ---->∞

Now look at the 1/√n term
as as n ---->∞ , 1/√n -----> 0
e.g. let n = 10,000,000 , 1/√10,000,000 = .00031... getting small

So you are left with
lim (0 + 1)/(0 - 1) as n ---->∞
= -1