In Axx vs Kxxx (declarer vs dummy) the standard safe play to check opponents split (3-3 or 4-2) is to use blank trick (x from both hands) before using A, K and see if last x is the last in the suit. No risk to give a trick if opponents have 4-2 split in the suit. So just play x-x from in both suits than use AK to check the split in opponents hands. I suppose the hand has no problem to win the lead, play x to x in one suit, win next trick, play x to x in 2nd 4-3 suit and win next trick - you have 2 losers and time to check both 4-3 suits. The only risk is that opponents may develop a winner to be played at trick 5. I am not expert at table but I read a lot and solved problems, so I hope my post here answer pretty well to the question. The real hand has some problems. The 9 tricks are based on LHO having DQ - 4 in D with finesse, + 5 top cards in the other 3 suits. SJ make proper to test H split but a club return next release a trick (or more) for opponents. Would be nice that small to small trick in heart to be given to LHO (if lead was not in clubs will have a reason to refrain to do it now). Spades can give 3 tricks not only for 3-3. If opponents have Qx vs T9xx proper play is A,K,2 to J and standard play fails. It is not just math for two 4-3 suits to be in opponents hands 3-3 or 4-2.