HONG KONG — For American technology companies from Microsoft to Facebook to Google, China is a difficult, even impossible, place to operate.

But one company, the social network LinkedIn, has found a way to do business — by being willing to compromise on the free expression that is the backbone of life on the Western Internet.

LinkedIn’s experience provides a blueprint, and perhaps a cautionary lesson, for Silicon Valley as it tries to crack the vast Chinese market. Other American tech companies are watching with great interest, wondering whether LinkedIn will find an equilibrium between free speech and Chinese law that it can live with.

“Over the next five years, things will continue to progress in a positive fashion over there, so it’s important to be there today,” said Kerry Rice, an Internet analyst at Needham, a brokerage firm. “If LinkedIn figures out how to navigate the operating environment in China, clearly other companies will try to imitate that.”