We learn from the Chanukas ha'Bayis of Shlomo ha'Melech that it is forbidden to mix one Simchah with another.
The year that Shlomo ha'Melech made the Chanukas ha'Bayis, Klal Yisrael did not fast on Yom Kippur. (1)
At the time that Shlomo ha'Melech tired to place the Aron in the Beis ha'Mikdash the gates refused to open and stayed that way until he mentioned the Chesed of his father David. (2)
A person should only interrupt learning Torah for the sake of a Mitzvah if the Mitzvah can’t be done by someone else.
A woman may put on cosmetics on Chol ha'Mo'ed even if she is an older woman. (3)
Rebbi Yehudah says that a woman may not pot on foundation on Chol ha’Mo’ed however if she will remove the foundation before the end of Mo'ed it is permitted.
A BIT MORE
1. The year that Klal Yisrael did not fast on Yon Kippur they were concerned that they would be punished until a Bas Kol said that everybody is primed for the world to come.
2. Shlomo ha'Melech said 24 Renanos and the gates of the Beis ha'Mikdash did not open, he said “The gates shall lift their heads” and they still did not open. The gates only opened at the mention of the Chesed of David ha'Melech and at that instant everybody knew that David ha'Melech had been forgiven for his sin.
3. A sixty year old woman enjoys music just like a six year old and accordingly it is appropriate for her to wear cosmetics.
The Gemara says that a student that takes leave from his Rebbi and subsequently stays in town overnight must take leave again. This is learned from Klal Yisrael that took leave from Shlomo ha'Melech on Shemini Atzeres and than again on the next day. The Bach asks why did Klal Yisrael take leave on Shemini Atzeres from Shlomo ha'Melech if they knew that they would not leave Yerushalayim until the next day given that the Halachah dictates that Shemini Atzeres requires Linah (an overnight stay in Yerushalayim) and they would have to take leave the day after Shemini Atzeres again. The answer is that which the Gemara says that if you take leave and stay overnight you must take leave again that’s only if you stay over an extra day that was not originally planned. But if you leave on the next day as planned it is not necessary to take leave again. Klal Yisrael ended up staying over until two days after Shemini Atzeres and thus they were require to take leave on the day after Shemini Atzeres for a second time. However if they had left on the day after Shemini Atzeres as planned they would not have had to take leave again. (Ran, Hagahos ha'Bach on the Ran, Taz)
Students that takes leave from the Rebbi and stay in town overnight must take leave again the next day. However that is only if he did not tell his Rebbi originally that he plans on staying overnight, but if at the time he took leave he told him that he plans on staying overnight there is no need to take leave a second time. (Shulchan Aruch YD 242:31)