How to play AKJx opposite xxx for 3 tricks at matchpoints
The best line for maximum tricks is to cash the Ace and then finesses the Jack. This has an 18% chance of success and averages 2.87 tricks per occurrence (from hardcopy of The Bridge Encyclopedia). This is a losing play in Matchpoints; unless other considerations exist.

The real trick in Matchpoints is to make losing plays that work, and avoid winning plays that fail. Barry Crane is alleged to have been able, when he really needed a top, to incite a revoke from opponents. ;-)

However, making these subtle choices requires complete information on the hand. Not to be rude, but the fact that you are asking this question, a rather basic one on declarer play, without specifying the other conditions suggests that you actually have no idea how to judge if a contract is normal or not. There are several contributors on this site who can help you learn how to properly make those judgements, if you can provide more detailed information.

For this particular card combination, I would much rather be looking for a squeeze or endplay to get my extra trick. That requires an exact count of opponents distribution as well as our own, and a better than random guess at the high point locations. I also need to know how hard to try for the extra trick. Hence all the questions asked in my comment above.

Let's review some basic end game techniques to emphasize why full disclosure of the hand is necessary. Fundamental to all Squeezes is rectifying the count, meaning losing the desired full number of losers early. Fundamental to all Throw-Ins is losing the desired full number of losers late, possibly to a specific opponent. What are my prospects of doing so on a given hand? Only after that is answered does one even begin to think about taking optional random finesses.



More on Crane, for anyone interested, by Grant Baze, who was one of his regular partners.