Define f: (-1,1) -> R by f(x) = x+1/x^2-1. Does f have a limit at 1? Justify

I believe that there is no Limit at 1 their is an asymptote at 1 because if I factor I am left with 1/x-1. Am I able to say is this proof good enough to say this or do i need to prove tis a different way

Assume there is a Limit of f at 1 Choose E = 1/4. There is a @>0 such that if

0<abs(x-1)<@ then abs(f(x)-L) < 1/4 choose a p= -@/4 and q= @/4 then f(p)= -1

f(q)= 1 so 2 = abs(f(p)-f(q)) <= abs(f(p)-L) + abs(L-f(q))< 1/4 + 1/4 = 1/2