Excerpts from Books and Wikipedia
"The tension between Moscow and Beijing had been exposed by fighting along their frontier on the Ussiri River in March 1969. This was a conflict the United States might exploit. Also, Mao could see the advantages of a friendly superpower to counterbalance Soviet hostility. . . . The major problem was Taiwan, recognized by the United States as having the legitimate government of China and seen by Mao as a rebellious province. As neither side could concede on this matter, a formula to evade the issue had to be agreed. In reality, this prepared the way for the official recognition of the People's Republic, which saw China gaining a permanent seat on the United Nations Security Council. . . . Nixon's coup led to a significant relaxation of Cold War tensions." [Furtado: 1001 Days]