Question

Sam and edith have a friendly​ rivalry: he's a better golfer than​ _____, but​ she's a better tennis player than​ _____.

Answer 1

We can complete the first space with her or she (is); and the second space with him or he (is). Usually the forms than her/than him are more colloquial and the forms than she (is)/than he (is) are more formal, But both are correct.

He's a better golfer than her (or than she (is).

She's a better tennis player than him (or than he (is).

Answer 2

The correct answer in the spaces provided is her and him. To complete the sentence, it should be read as, "He's a better golfer than her, but she's a better tennis player than him." This is the correct structure of the sentence.