a) To solve the expression 5/6 + 7/9 - 5/6 + 1/6, we can combine like terms:

5/6 + 7/9 - 5/6 + 1/6 = (5/6 - 5/6) + 7/9 + 1/6
= 0 + 7/9 + 1/6

To add these fractions, we need to find a common denominator. The least common multiple of 9 and 6 is 18.

= (7/9)(2/2) + (1/6)(3/3)
= 14/18 + 3/18
= 17/18

Therefore, the result is 17/18.

b) To solve the expression 8/11 * 7/8 + 8/11 / 4/5, we can simplify each operation separately:

8/11 * 7/8 = (8 * 7) / (11 * 8)
= 56/88
= 7/11

8/11 / 4/5 = (8/11) * (5/4)
= (8 * 5) / (11 * 4)
= 40/44
= 10/11

Now, we can add the results:

7/11 + 10/11 = (7 + 10) / 11
= 17/11

Therefore, the result is 17/11.