They are three different religions. Although Christianity also uses the Old Testament. Obviously, Jews aren't going to use the New Testament. And Islam was founded by another person, with different beliefs too.
They are different. Muslims believe Jesus was raised to the heavens but Christians say he was crucified by the Jewish(No offense to any Jewish). Christian believe that Jesus was the son of God but muslims don't. Christians also say there are three things that combine to make one God which are The Holy Spirit, Jesus and God himself but muslims believe that there is only one god and there was a prophet after Jesus. (Sorry I only gave facts about two of the three, I don't really know much about Jewish).
Because they are all written by men and are not inspired by a higher power, if there was a book inspired by an all knowing, all powerful, omnipresent being we would know it to our core, everyone, everywhere would follow the same faith because such a being would know how to make its message known without doubt. Since they were written by man, they are also doubted by man.
They worship different gods. You would not call a statue of Pan and one of Apollo the same god so why would you say separate books worship the same god when they produce different and contradicting religions?
Because the Torah, the Psalms, and the Gospel of Jesus Christ do not exist in their original forms. The present-day editions are only interpretations by their respective followers of later ages. Thus God's Plan has come to pass which is mentioned in the Bible "I will send them a prophet from their Brethren and I will put my words in his mouth and what ever he speaks he will speak in my name and any one who does not harken to his words which he will speak in my name I WILL REQUIRE IT OF HIM" Deut 18:18.
So the Quran is the final and the complete code of Religion, and is and will be preserved for all time absolutely intact in its original form.
"We have without doubt, sent down the message and We will assuredly guard it (from corruption.)" Quran 15:9