General Electric Co. is considering breaking itself apart, a dramatic move that would mark the end of one of the oldest and largest U.S. conglomerates.

The 125-year-old business, which was once the most valuable U.S. company and still employs about 300,000 people, sells everything from airplane engines to hospital incubators. But in the past year the company that came to embody America’s industrial power has fallen on hard times, prompting it to change CEOs, sell assets and slash its dividend.

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