Calculate the value of the expression: (17 51/94 - 25 5/18) - (19 51/94 - 2 3/10)

Let's calculate the value of the expression step by step:

1. Rewrite the expression: $$ (17 \frac{51}{94} - 25 \frac{5}{18}) - (19 \frac{51}{94} - 2 \frac{3}{10}) $$
2. Group similar terms:

   Group the whole numbers and the fractions together:

   $$ (17 - 25) + (\frac{51}{94} - \frac{5}{18}) - (19 - 2) - (\frac{51}{94} - \frac{3}{10}) $$ $$ -8 + (\frac{51}{94} - \frac{5}{18}) - 17 - (\frac{51}{94} - \frac{3}{10}) $$
3. Distribute the negative sign: $$ -8 + \frac{51}{94} - \frac{5}{18} - 17 - \frac{51}{94} + \frac{3}{10} $$
4. Combine like terms: $$ (-8 - 17) + (\frac{51}{94} - \frac{51}{94}) + (\frac{3}{10} - \frac{5}{18}) $$ $$ -25 + 0 + (\frac{3}{10} - \frac{5}{18}) $$
5. Find a common denominator for the fractions:

   The least common multiple of 10 and 18 is 90.

   $$ \frac{3}{10} = \frac{3 \times 9}{10 \times 9} = \frac{27}{90} $$ $$ \frac{5}{18} = \frac{5 \times 5}{18 \times 5} = \frac{25}{90} $$
6. Subtract the fractions: $$ \frac{27}{90} - \frac{25}{90} = \frac{27 - 25}{90} = \frac{2}{90} = \frac{1}{45} $$
7. Final result: $$ -25 + \frac{1}{45} = -24 \frac{44}{45} $$

So, the final answer is: