Jesus' Birth - Jerusalem or Bethlehem?

A Very simple aspect of Christianity is that Jesus was born in bethlehem. But, in Mormonism, we have a little bit of a contradiction - Was He?

Bethlehem:
(Bible) Matthew 2:1 "After Jesus was born in born in Bethlehem of Judea..."
(Bible) Micah 5:2 "But You, Bethlehem Ephrathah...Out of You will come the one to be Ruler over Israel..."

Jerusalem:
(Book of Mormon) Alma 7:10 "And Behold, He shall be born of Mary, at Jerusalem, the Land of our Forefathers..."

A common Mormon argument about this particular verse is that, since the verse says "at Jerusalem" rather than "in Jerusalem" that it is referring to the Land of Jerusalem, which stretched farther than the actual city. This would be a valid argument, if Bethlehem was actually in that Land.
At that time, The Land and city of Jerusalem was part of The Kingdom of Judah, while bethlehem was located in Judea. Two different places. Bethlehem was obviously not part of Jerusalem in any way.

http://www.YouTube.com/user/JewForJesusAlways