To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the expression inside the parentheses:

11 and 94/1591 - 6 and 38/1517

To subtract mixed numbers, we need to find a common denominator. The common denominator for 1591 and 1517 is 1591 * 1517 = 2,408,647.

11 and 94/1591 - 6 and 38/1517 becomes:

(11 * 1517 + 94) / 2408647 - (6 * 1591 + 38) / 2408647

(16787 + 94) / 2408647 - (9546 + 38) / 2408647

16881 / 2408647 - 9584 / 2408647

Now, let's simplify the expression further:

5/6 x (16881 / 2408647)

To multiply fractions, we multiply the numerators together and the denominators together.

5/6 x 16881 / 2408647

(5 * 16881) / (6 * 2408647)

84405 / 14451882

Now, let's simplify the expression further:

5/6 + 84405 / 14451882

To add fractions, we need to find a common denominator. The common denominator for 6 and 14451882 is 6 * 14451882 = 86711292.

5/6 + 84405 / 14451882 becomes:

(5 * 14451882 + 84405) / 86711292

(72259410 + 84405) / 86711292

72343815 / 86711292

Finally, let's simplify the expression further:

72343815 / 86711292 : 8 and 11/43

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

72343815 / 86711292 x 43/ (8 * 43 + 11)

72343815 / 86711292 x 43/ 347

(72343815 * 43) / (86711292 * 347)

3109926945 / 30099464284

Therefore, the simplified expression is 3109926945 / 30099464284.