is an expression that nominalizes what comes before it (turns it into a noun-phrase), and then highlights something about that (A) phrase. In the case of ことができる
, the thing being highlighted about (A) is that it is ‘possible’. This translates as ‘can do (A)’, or ‘to be able to do (A)’.
is only required when the (A) phrase needs nominalization (is not a noun to begin with). Due to this, ができる
may be used by itself when following a noun, without changing the meaning.
I want a boyfriend that can drive.
We are looking for a person that is able to do physical labor.
のが (or のは) is also frequently used for nominalization, but this is rarely the case when a verb follows it. Some other expressions where のが may not be swapped for こと are as follows:
ことがある - For (A) to exist.
ことにする - To make something (A).
ことになる - For (A) to come to be.