Complex sentence: The U.S. and its allies believed that Osama bin Laden was hiding in the mountains at Tora Bora, but despite overrunning the Taliban and al-Qaeda positions and hearing bin Laden's voice in intercepted radio transmissions several times, they failed to kill or capture him.
Split into simpler sentences: The U.S. and its allies believed that Osama bin Laden was hiding in the mountains at Tora Bora, and overran Taliban and al-Qaeda positions. Although the allies heard bin Laden's voice in intercepted radio transmissions several times, they failed to kill or capture him.