Is it correct the following example of the relationship between classical mechanics and modern physics?

Strictly speaking, you can’t combine velocities with (v1 + v2). (v1 + v2) / (1 + (v1 * v2) / c^2)
is the actual equation. Of course, the sort of velocities we encounter in day-to-day life don’t come close to c^{2, which is the speed of light squared. That means that (1 + (v1 * v2) / c}2).
Since that would mean dividing by 1, it’s usually okay to just skip that step and use (v1 + v2). In most situation it works, even if it’s not technically correct. Have I missed anything?