אך שמח 1 – It says in Meseches Sukkah 48a that from the words, "אך שמח" in Devorim 16:15 it comes to include that the night of the last days of Yom Tov must also include Simcha, joy. Many wonder how the Gemara can learn this from the word, "אך" – for this word is generally used to exclude things and not to include things – which is what the Gemara is doing here – it is saying that the word comes to include the last night of Sukkos in the obligation of joy. As it says in Yerushalmi Brochos 9:5 "אכין ורקין מיעוטין הן" – the Lashon of "אך" and "רק" are Leshonos of excluding, not including. It says in Parshas Emor 23:36 "ביום השמיני מקרא קודש יהיה לכם, והקרבתם אשה לד' עצרת היא" – "On the eighth day you shall observe a sacred occasion and bring an offering by fire to Hashem; it is a solemn gathering." Rashi explains that it is like a king who invited his sons to a banquet for a certain amount of days. When the time came for the sons to leave, the father said to them: My sons, I request of you, stay with me for one more day for your departure is difficult for me to bear. We need to understand this, why Hakodosh Boruch Hu asks Klal Yisroel to remain one more day, after the completion of the Yom Tov of Sukkos?
The Sefer Tiferes Bonim explains a Midrash Pliah, on Sefer Iyov. Iyov was complaining about his Yisurim, the afflictions that came upon him, until Hakodosh Boruch Hu showed Iyov a Sukkah with two complete walls, and a third wall which was a Tefach – which as per Halacha is a Kosher Sukkah. What is the meaning of this cryptic Midrash? The מהר"ש ממונקאטש explains that if one has a certain Tzarah or is lacking something, he should remember that which the Shem Hashem is lacking, for the Name of Hashem is not complete in this world until Amalek is eradicated and Moshiach will come. The Posuk says, "כי יד על כס י-ה" that the Shem Hashem currently only has in this world the letters 'י and 'ה and is missing the 'ו and the 'ה to spell the complete Shem Havayah of Hakodosh Boruch Hu. One should be Mispalel for Rachamim for the Shem Hashem, that its deficiency in this world should be filled. The minimum dimension of a Sukkah is seven by seven Tefachim. If one has two walls of seven Tefachim each, plus the third wall, in order to be Kosher it only needs to be a partial wall, a Tefach – the total Tefachim is fifteen Tefachim, which is the Gematria of ה-י. Hakodosh Boruch Hu showed Iyov a Sukkah with two walls and a partial third wall, a total of fifteen Tefachim, to allude to Iyov that he should be Mispalel for the ה-י for the Shem Hashem, which is lacking the ה-ו. If one does so, then after that, he can be Mispalel for his own needs and that which he is lacking, and he will have a Yeshuah – a salvation.
The Gemara in Sukkah 27a says: Rebbe Eliezer says that one is obligated to eat fourteen Seudos in the Sukkah, one every day and one every night (seven days of Sukkos – thus a total of fourteen Seudos). The Posuk says, "אך שמח" which Chazal Darshen – "לרבות לילי יום טוב האחרון לשמחה" - that it comes to include the night of the last days of Yom Tov, that Simcha is required. Rashi in Pesachim 71a says that it is specifically the night of the last days of Yom Tov, which is included in the obligation of Simcha, but not the last day. Thus, only one Seudah is added to the rest of the days of Yom Tov. There were fourteen Seudos on Sukkos, and one on Shemini Atzeres night, for a total of fifteen Seudos, which is the Gematria of the Shem Hashem ה-י. Like by Iyov, this is to remind us about the Shem Hashem, which is only ה-י in this world, and is lacking the ה"ו. Specifically, on Shemini Atzeres, we are to be Mispalel to Hakodosh Boruch Hu that His Name should be completed in this world. With this understanding, we can explain why the Torah uses a Loshon of אך when it teaches us about including Shemini Atzeres in the obligation of Simcha. The Torah uses a Loshon of אך, which is a Loshon of lacking, for by adding the Simcha obligation, the Seudah on Shemini Atzeres, it is to remind us about what is lacking – the Shem Hashem. We must be Mispalel for the Geulah to come, so that the Name of Hashem can be complete in this world. With this we can explain the words of Rashi. Hakodosh Boruch Hu says to Klal Yisroel, "עכבו עמי" – remain with Me – for My sake, one more day. Have one more Seudah so that you get to the number "fifteen" – and then you will remember that My Name is incomplete – in this world there is now only the ה-י. We must beseech Hakodosh Boruch Hu to make His Name complete – that the Geulah should come, and His Name in this world will be complete, and the Glory of Hakodosh Boruch Hu will be known to all.