How does rationalizing the denominator use the form of 1?
you can always multiply by 1 without changing the value. So, you want something that makes the denominator rational.
(3+√7)/(2-√7) * (2+√7)/(2+√7)
= (3+√7)(2+√7) / (2-√7)(2+√7)
= (13+5√7)/-3
(2-3i)/(6+i) * (6-i)/(6-i)
= (2-3i)(6-i) / (6+i)(6-i)
= (15-20i)/37