9) 17 + 14 - 19 - 1

1. Convert mixed numbers to improper fractions: $$17\frac{2}{3} = \frac{53}{3}$$, $$14\frac{3}{8} = \frac{115}{8}$$, $$19\frac{5}{9} = \frac{176}{9}$$, $$1\frac{1}{36} = \frac{37}{36}$$.
2. Find a common denominator (72): $$\frac{53}{3} = \frac{1272}{72}$$, $$\frac{115}{8} = \frac{1035}{72}$$, $$\frac{176}{9} = \frac{1408}{72}$$, $$\frac{37}{36} = \frac{74}{72}$$.
3. Perform operations: $$\frac{1272}{72} + \frac{1035}{72} - \frac{1408}{72} - \frac{74}{72} = \frac{2307}{72} - \frac{1408}{72} - \frac{74}{72} = \frac{899}{72} - \frac{74}{72} = \frac{825}{72} = \frac{275}{24} = 11\frac{11}{24}$$.