To solve the first equation:
1/3 + 4/5 - 1/12

We need to find a common denominator for all the fractions, which in this case is 60.

Rewriting the fractions with the common denominator:
20/60 + 48/60 - 5/60

Performing addition:
20/60 + 48/60 = 68/60
68/60 - 5/60 = 63/60

63/60 simplifies to 21/20

Therefore, 1/3 + 4/5 - 1/12 = 21/20

For the second equation:
2/7 - 1/6 + 1/9

Again, finding a common denominator which is 126:

Rewriting the fractions with the common denominator:
36/126 - 21/126 + 14/126

Performing subtraction:
36/126 - 21/126 = 15/126
15/126 + 14/126 = 29/126

Therefore, 2/7 - 1/6 + 1/9 = 29/126