Maple 13 calculator (whatever that is) knows squat about good tricks in mathematics: throw it away.

After you simplify the expression for f'(a) within the limit you get:

[Sqrt(a+2) - Sqrt(a+h+2)]/[h*sqrt(a+2)sqrt(a+h+2)] .

Multiply the above by the numerator's conjugate (the same expression as the numerator but with a + sign instead the - one) and simplify. You get an expression perfectly well defined and continuous when h --> 0 and thus you can directly substitute h = 0 and get what you want.

Tonio