Daf Yomi - Sukkah 25 - Osek B'mitzva by Reb Jay

Shluchei mitzva are patur from sitting in the sukka, because of
oseik b'mitzva patur min hamitzva. Rashi writes that this refers
to going to learn Torah, or to see his Rebbi, or pidyon shevuyim.
Tosfos notes that he is patur from the sukka only in a case
where if he would sit in the sukka, he would be dealyed or
unable to perform these other mitzvos, otherwise, there is no
patur of oseik b'mitzva patur min hamitzva. The Ran writes that
while a person is being Oisek bmitzva, he is patur from other
mitzvos, even if it is possible to fulfill both of them. This is the
reason, writes the Ran, that a groom is patur from krias Shema,
as although he could find the time to say it, since he is tarud in a
mitzva, the Torah does not obligate him to do another mitzva. A
nafka mina between Tosfos and the Ran would be
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a person on
the way to do pidyon shevuyim who finds a lost object, and the
owner of the object will be at the destination of the person going
to do pidyon shevuyim. Tosfos would say that since doing the
mitzva of hashavas aveida doess not delay the mitzva of pidyon
shevuyim, he is obligated in the mitzva, while the Ran would
say that since he is involved in the mitzva of pidyon shevuyim,
the Torah is not mechayev him whatsoever in the mitzva of
pidyon shevuyim (today, in any case, we have lost the ability to
be so focused on one mitzva, and even the Ran would agree that
he is obligated in the mitzva). Rav Akiva Eiger asks how can the
Gemara learn the limud of oseik b'mitzva patur min hamitzva
from a groom and from Korban Pesach (that those who were
oisek with the coffin of Yoseph were patur from the Korban
Pesach), both those cases involve a shev v'al tasay, while the
case of sukka involves a lo sa'asay of eating outside the sukka?
Rav Akiva Eiger answers that there is no lo sa'asay of eating
outside the sukka, only an asay to eat in the sukka, and if a
person eats outside the sukka, he is mevatel an asay which is a
shev v'al tasay, so there is no problem. Another answer could
be, that while Korban Pesach is a mitzvos asay, it is an asay
sheyeish bo kares (the only other asay that has a chiyuv of kares
for not performing the mitzva is Bris Milah), which gives it a
similarity to a lo sa'asay, and is thus a good rayah.
Rav Moshe Shternbuch asks why is a person required to stop
davening to answer, or in some cases merely stop davening and
listen to (depending on where he is up to)kedusha, he is Oisek
bmitzva and is therefore patur from other mitzvos? He answers
that a person is patur from a mitzva only when he is being oisek
in a different mitzva, but if it is part of the same mitzva--in this
case tefila--he is chayov.