Can I write off a business trip that I combined with a personal vacation?

Partly. For domestic travel, if the primary purpose of the trip is business, your round-trip transportation is fully deductible even if you tack on personal days, but you can only deduct lodging, meals, and local costs for the business days. If the trip is primarily personal, the transportation is not deductible, though specific business expenses incurred there still are. The IRS looks at the number of days spent on business versus pleasure to judge the primary purpose. International trips have stricter rules and may require prorating even the airfare. Keep an itinerary, meeting notes, and receipts that clearly separate the business days, because mixing the two is a favorite audit area.