Question

root 2 plus root 3/3 root 2 - 2 root 3

Answer 1

Here typing mistake , I think
question is
(√2 + √3)/( 3√2 -2√3) = a -b√6

( √2 + √3)( 3√2 + 2√3)/{ (3√2)² - (2√3)² }

(6 + 3√6 + 2√6 + 6 )/( 18 - 12)

(12 + 5√6)/6

2 +( 5/12)√6 = a - b√6

so, a = 2 and b = - 5/12