Can someone explain this?

If MacDonald makes a 10% down payment, then the most he can pay for his new home = $191,517.76 / (1 - 0.10) = $212,797.51 ≈ $212,800. So, is it similar to discounting when someone makes a down payment ? I would like to know how the denominator (1-0.10) came in to existence. I know it’s fundamental question but I’m trying to have a strong foundation. Thanks in advance.

Amount of Loan * (1-.10) = 191,517.76 Adjusted = Amount of Loan = 191,517.76/(1-.10)

Boy! The closer I get, the more I doubt my fundamentals. It will NOT happen again. Thanks man