NEW YORK — T-Mobile and MetroPCS have agreed to combine their struggling cellphone businesses in a deal aimed at letting them compete better with their three larger rivals.

The combined company will use the ­T-Mobile brand and have about 42.5 million subscribers. Although T-Mobile will stay number four among US wireless companies, it will get access to more space on the airwaves, a critical factor as cellphone carriers try to expand their capacity for wireless broadband.