If ` (7 + 4 sqrt(3))^(n) + 5 + t ` , where n and s are
positive integers and t is a proper fraction , show that
(1 - t) (s + t) = 1

Explanation

To solve the problem, we need to show that \( (1 - t)(s + t) = 1 \) given that \( (7 + 4\sqrt{3})^n = s + t \), where \( n \) and \( s \) are positive integers and \( t \) is a proper fraction.

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ s + t = (7 + 4\sqrt{3})^n \]
...