Complex sentence: Mossadegh prolonged his visit on Washington's urging because the US administration believed that the upcoming conservative government of Churchill would be amicable to this deal, but the deal was rejected by the British, who believed Mossadegh's downfall was imminent.
Split into simpler sentences: Mossadegh prolonged his visit on Washington's urging because the US administration believed that the incoming Conservative government of Churchill would be agreeable to that deal. However, the deal was rejected by the British, who believed Mossadegh's downfall was imminent.