To simplify this expression, we'll start by converting all the mixed numbers to improper fractions:

17/18 = 1.94444
13/14 = 1.92857
5/8 = 0.625
19/20 = 0.95
25/78 = 0.32051
1/26 = 0.03846

Now, we can rewrite the expression with the improper fractions:

(1.94444 - 1.92857 - 0.625 ÷ 0.95) ÷ (0.32051 - 0.03846)

Next, we'll perform the operations inside the parentheses:

(0.01687 - 0.625 ÷ 0.95) ÷ (0.32051 - 0.03846)
(0.01687 - 0.65789) ÷ (0.28205)
(-0.64102) ÷ (0.28205)
-2.27136

Therefore, the simplified result is -2.27136.