A discontinuity is removable if the limit exists

Remember Continuity means lim x->a f(x) = f(a)

which implies

1. f(a) is defined

2. lim x->a f(x)

3. 1 = 2

For example

f(x)=(x+3)/(x^2-9)

limas x->-3 = -1/6 so if we define f(-3) =-1/6 all conditions are met

limasx->3 DNE fails 2 cannot remove discontinuity