Write Smart! No Comma Here

If the second part of the sentence isn’t a sentence, don’t use a comma. Example: John ate the chili and burped loudly. (“and burped loudly” is not a sentence- it has no subject, so there is no comma before the “and.”)

Example: The dog and cat fought but made up. However, if you change that last example to The dog and cat fought, but they made up, it now needs a comma because you’ve added a subject (they) to the second part and made it into an independent clause, then joined them with "but" (a conjunction).

The second part is called a subordinate clause (it will not stand alone). Some examples are:
...and gave the dog a bone.
...for two days and an hour.
...but wasn't able to keep up.
...and found the restaurant on a side street.