Learn Spanish (Latin America): Ella confirmó que expandirían el negocio rentable. - She confirmed that they would expand the profitable business.

This sentence uses reported speech. If the original quote was a future promise like expandirán (they will expand), reporting it after a past tense verb like confirmó (she confirmed) changes that future tense into the conditional tense expandirían (they would expand).

How do you build the conditional tense for expandirían?

To make the conditional (meaning would do something), you take the full infinitive of the verb, which is expandir, and attach the appropriate ending. For the they form, you add -ían to get expandirían.

How do we know who is doing the expanding if there is no word for they?

The -ían ending on expandirían already tells us the subject is they (ellos or ellas) or you all (ustedes). Because Spanish verb endings give away the subject, pronouns are usually dropped unless you need them for contrast or clarity.

Does rentable relate to the English word rent?