Add. Simplify if possible.
3z/z^2-4 + z/z-2 =
Not sure if it would be 3z/z^2.
Just like with numbers you will need a common denominator.
Since z^2 - 4 = (z+2)(z-2) and z-2 is the other denominator, it will be z^2-4
3z/(z^2-4) + z/(z-2) , notice I corrected your typing
=
3z/(z^2-4) + z(z+2)/(z^2-4)
= (z^2 + 5z)/(z^2-4) or z(z+5)/((z+2)(z-2))