Question

F(X)= x-2/(x^2-4) is continuous at x=1 and why as limits approach from 1+ and 1-

Answer 1

why what?

limit as x -> 1 from either side is

(-1-2)/(1-4) = -3/-3 = 1

one would expect this, as f is continuous.

Answer 2

oops. I did x -> -1

limit as x -> 1 is

(1-2)/(1-4) = 1/3

Makes sense, since f(x) = 1/(x+2) for x ≠ ±2