To calculate this expression, we first need to convert the mixed numbers into improper fractions.

1 2/9 = 11/9
1 1/6 = 7/6
1 25/42 = 67/42

Now we can calculate:

$11/9+7/6$ $2-67/42$ = $22/18+21/18$ $84/42-67/42$ = $43/18$ $17/42$ = $43/18$ $17/42$ = 731/756

Therefore, the result is 731/756.