3. What could Nixon hope to gain by establishing better relations with Communist China?

He wants to enhance relationships with China.

Explanation:

President Nixon made efforts to improve relations with Communist China to put pressure on the Soviet Union to cooperate more with the United States. Both Communist China and the Soviet Union were strong, communist countries. President Nixon believed if we became friendlier with Communist China, the Soviet Union would want to work closer with us because they would be fearful we might start favoring Communist China.