To simplify the expression, we first need to find the result of the operations within the parentheses:

7/8 + 3/4 = 7/8 + 6/8 = 13/8

Now we can substitute this result back into the original expression:

9(13/8) - 1 - (5/6 25/48)

To simplify this further:

9*(13/8) = 117/8

Now our expression becomes:

117/8 - 1 - (5/6*25/48)

To simplify the remaining operations:

117/8 - 1 = 117/8 - 8/8 = 109/8

Now we have:

109/8 - 5/6 * 25/48

To multiply the fractions:

5/6 * 25/48 = 125/288

So now our expression becomes:

109/8 - 125/288

To subtract the fractions:

109/8 - 125/288 = 2919/288 - 125/288 = 2794/288

Finally, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor of 2:

2794 ÷ 2 = 1397
288 ÷ 2 = 144

Therefore, the final result of the expression is:

1397/144 or approximately 9.7014.