1. Lyft began a partnership with rental car company Sixt to let users access rental cars.

2. Lyft began a partnership with a rental car company Sixt to let users access rental cars.
3. Lyft began a partnership with the rental car company Sixt to let users access rental cars.
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Which one do we have to use in the sentences?
1. rental car company
2. a rental car company
3. the rental car company

Since you are naming the company, use #3.

Also, there should be commas before and after "Sixt" since it's an appositive.

#1 is also often used

#2 would definitely require commas.

All three options can be grammatically correct, but the one you choose would depend on the specific context and meaning you want to convey in your sentences.

1. "Rental car company"
Using "rental car company" without any article (a, an, the) is a more general way of referring to a company that operates in the rental car industry. This option implies that Lyft has partnered with any rental car company in general, without specifying a particular one.

2. "A rental car company"
Adding the indefinite article "a" before "rental car company" specifies that Lyft has partnered with one rental car company, but it doesn't indicate a specific one. This option suggests that Lyft has entered into a partnership with just any one rental car company, but the specific company is not important or hasn't been mentioned before.

3. "The rental car company"
Using the definite article "the" before "rental car company" signifies that Lyft has partnered with a specific rental car company, which has most likely been mentioned or is well-known. This option indicates that there is one particular rental car company called Sixt that has partnered with Lyft.

In summary, if you want to convey that Lyft has partnered with any rental car company in general, you can use option 1. If you want to indicate that Lyft has partnered with one rental car company specifically but it doesn't matter which one, you can use option 2. If you want to specify that Lyft has partnered with a particular rental car company named Sixt, you can use option 3.