(2 + sqrt 2)/(2 - sqrt 2) = (x)/(3 + sqrt 10)
How to solve for x?
(2+√2)/(2-√2) = x/(3+√10)
just multiply by 3+√10 and you have
x = (2+√2)(3+√10)/(2-√2)
= (26+3√2+2√10)/(2-√2)
now multiply top and bottom by 2+√2 and you have
x = (26+3√2+2√10)(2+√2)/2
= 58+32√2+4√5+4√10
you can massage that in many ways, such as:
58 + 32√2 + 4√5 (1+√2)
58 + 4√2 (8+2√5) + 4√5
and so on. The very first result might just be the simplest.