Palestine has as valid a claim to Jerusalem as Israel does:

The Palestinians have as valid a claim to Jerusalem as the capitol of their state as the Israelis has a claim to Jerusalem as the capitol of their state. At the end of 2008, the population of East Jerusalem was 57% Muslim (Palestinian) and only 43% Jewish, sowing a clear and workable Palestinian majority in East Jerusalem.(10) Both sides have important religious sites in the city. The dome of the Rock is integral to Islam to the prophet Muhammad’s night journey to the temple making it Islam’s third holiest place after only Mecca and Medina. It is equally important for Jews to have access to the Western Wall.(1) For the Palestinians Israel has made its claim over the whole of Jerusalem more illegitimate by misgoverning the East of Jerusalem. For example, because there are no Arab’s on the committee that chooses street names in Jerusalem in the telephone book maps of Arab neighbourhoods are blank, like unexplored parts of the Amazon in the 19th century. As a result mail is seldom delivered there, and having Arabs' become perceived to be  invisible, non-existent or else branded as terrorists.(5) Throughout the Israeli occupation the demographic balance has served as the main consideration in Israeli decision making for both local and central government. This has been a deliberate attempt to forstall any attempt by the Palestinians to claim that they have an equal right to Jerusalem. Israeli policies have been directed to mainly serve spatial/demographic domination of "Jewish Jerusalem." There was no attempt to "integrate" the Palestinian neighborhoods' functions with West Jerusalem or the settlements built in Palestinian areas. On the contrary, the policy has been to separate and isolate them. East Jerusalem serves naturally as a metropolitan center of the entire West Bank, until the Oslo agreement in September 1993, some autonomy of Palestinian Jerusalemites was allowed especially in educational, sport, health, cultural, religious institutions and community based organizations. There has however been a movement from "United Jerusalem" to "Jewish Jerusalem." From 2000 the Palestinian demographic threat, became the reason for "getting rid" of Palestinian Jerusalemites after Israel had accomplished its spacio-political goals for a "Jewish Jerusalem." Israel of today is in the process of replacing the slogan of "United Jerusalem" with great "Jewish Jerusalem" with the Old City as its core. As a result of the Israeli policy, Palestinian neighborhoods (including the available land for future development) consist of only 17 percent of the entire East Jerusalem area and 7 percent of total municipal Jerusalem. Israel restricted the Palestinian construction and economic development, which led to the emigration of the Palestinians from the city to new areas developed as suburbs of the city. This territorial/demographic domination and restriction on Palestinian development affected East Jerusalem by deteriorating its functionality in disconnecting it from its hinterland and West Bank areas.(14) Israeli officials have also not been fair or protective of Palestinians,  repeatedly being highly abusive, and Israeli security forces have been accepting of abusive Israeli civilian treatment of Palestinians.(2) Moreover, Jerusalem can be shared, and thus divided in practical terms but not "divided" per se. It has been a Palestinian position that Jerusalem can "remain the capital of Israel" and can "remain undivided". This is a as long as that does not preclude the Palestinians from also having their capital in a "shared" city.(11) What matters is that it is recognised that the Palestinians have as valid a claim to their part of Jerusalem as the Israelis do to their part, and as a consequence Jerusalem  should be divided in such a way as to give the Palestinians control over their area as the capitol of their new state.