How do I remove these discontinuities?

So I understand how to find where a discontinuity is, but I am not sure how to remove it. Any tips?

Question 1: Identify and remove the discontinuities of f(x) = [sin(x+1) / tan(x+1)]

a) discontinuity at x = -1, remove by making f(-1)= 1

b) discontinuity at x = -1, can not removed

c) discontinuity at x = 0, remove by making f(0) = 1

d) discontinuity at x = 0, remove by making f(0) = 1

Question 2: Identify and remove the discontinuities of f(x) = [(x^3 - 3x^2 + 2x - 6) / (x - 3)]

a) discontinuity at x = 4, remove by making f(3) = 9

b) discontinuity at x = 4, can not remove

c) discontinuity at x = 3, remove by making f(3) = 11

d) discontinuity at x = 4, remove by making f(4) = 11

Any help is appreciated.