The government gave GMAC Financial Services another $3.8 billion in cash and took a majority stake in the auto lender, aiming to stabilize the company as it struggles with big losses in its home mortgage unit.

The fresh infusion is on top of $12.5 billion in taxpayer money Detroit-based GMAC has already received from the government. The new aid will boost the federal government’s ownership in GMAC to 56 percent, from 35 percent, and means the U.S. now holds a majority stake in three companies that it bailed out with taxpayer funds — GMAC, General Motors and insurer American International Group Inc. The government also has taken control of mortgage giants Fannie Mae and Freddie Mac.