Does the Book of Mormon contain the full gospel of Jesus Christ? David thought so:
Christ commanded the Nephites to write his teachings, for they were to come down to us as the fullness of his gospel to us. And why is it? Oh, why is it that you will not take the words of Christ himself, and lay down your contentions and disputations, taking his plain, simple teachings which he has given us in that book?
As you know, the teachings of Christ are the same in the New Testament and in the Book of Mormon.
But on account of the plain and precious things being taken from the Bible, there is room therein for disputations on some doctrinal points.
The teachings of Christ in the Book of Mormon are PURE, PLAIN, SIMPLE and FULL (David Whitmer, An Address to all Believers in Christ, p. 29).
Joseph said so:
34 He said there was a book deposited, written upon gold plates, giving an account of the former inhabitants of this continent, and the source from whence they sprang. He also said that the FULNESS OF THE EVERLASTING GOSPEL WAS CONTAINED IN IT, as delivered by the Savior to the ancient inhabitants; (JS-H 1)
2 Behold, I have manifested unto you, by my Spirit in many instances, that the THINGS WHICH YOU HAVE WRITTEN ARE TRUE; wherefore you know that they are true.
3 And if you know that they are true, behold, I GIVE UNTO YOU A COMMANDMENT, THAT YOU RELY UPON THE THINGS WHICH ARE WRITTEN;
4 For in them are ALL THINGS WRITTEN CONCERNING THE FOUNDATION OF MY CHURCH, MY GOSPEL, AND MY ROCK. (D&C 18, June 1829, “the foundation of” part was added later)
8 And gave him power from on high, by the means which were before prepared, to translate the Book of Mormon;
9 Which contains a record of a fallen people, and the FULNESS OF THE GOSPEL OF JESUS CHRIST to the Gentiles and to the Jews also; (D&C 20, April 1830)
The Book of Mormon said so:
24 And the angel of the Lord said unto me: Thou hast beheld that the book proceeded forth from the mouth of a Jew; and when it proceeded forth from the mouth of a Jew it contained the FULNESS OF THE GOSPEL of the Lord, of whom the twelve apostles bear record; and they bear record according to the truth which is in the Lamb of God.
25 Wherefore, these things go forth from the Jews in purity unto the Gentiles, according to the truth which is in God.
26 And after they go forth by the hand of the twelve apostles of the Lamb, from the Jews unto the Gentiles, thou seest the formation of that great and abominable church, which is most abominable above all other churches; for behold, they have taken away from the gospel of the Lamb many parts which are plain and most precious; and also many covenants of the Lord have they taken away.
35 For, behold, saith the Lamb: I will manifest myself unto thy seed, that they shall write many things which I shall minister unto them, which shall be plain and precious; and after thy seed shall be destroyed, and dwindle in unbelief, and also the seed of thy brethren, behold, these things shall be hid up, to come forth unto the Gentiles, by the gift and power of the Lamb.
36 And IN THEM SHALL BE WRITTEN MY GOSPEL, SAITH THE LAMB, AND MY ROCK AND MY SALVATION. (1 Nephi 13)
Then why did Joseph Smith add to the requirements of salvation by adding the Doctrine and Covenants?