9 1/2:(1 4/7-5/21*0.9) = 9 1/2:(1 4/7-4/ 21)
Convert all fractions to a common denominator, which is 21:

9 1/2:(1 4/7-4/21) = 19/2:(7/1 16/7 - 4/21)
= 19/2:(7 16/7 - 4/21)
= 19/2:(7 16/7 - 4/21)
= 19/2: (7 96/21 - 4/21)
= 19/2: (7 92/21)
= 19/2: (7 4 4/7)
= 19/2: (11 8/7)
= 19/2: (86/7)
= 19/2 * 7/86 = 133/172

Therefore, 9 1/2:(1 4/7-5/21*0.9) simplifies to 133/172.