\( ( ( \frac { 2 } { 2 } \div \frac { 3 } { 3 } ) - 1 ) - ( ( \frac { 2 } { 7 } \div 1 ) - \frac { 5 } { 3 } ) \div ( \frac { 2 } { 7 } , 1 ) \)

To simplify the expression \[ ( ( \frac { 2 } { 2 } \div \frac { 3 } { 3 } ) - 1 ) - ( ( \frac { 2 } { 7 } \div 1 ) - \frac { 5 } { 3 } ) \div ( \frac { 2 } { 7 } , 1 ) \] we will break it down step by step. 1. **Calculate \( \frac{2}{2} \div \frac{3}{3} \)**: \[ \frac{2}{2} = 1 \quad \text{and} \quad \frac{3}{3} = 1 \] Thus, \[ 1 \div 1 = 1 \] 2. **Now calculate \( (1 - 1) \)**: \[ 1 - 1 = 0 \] 3. **Next, calculate \( \frac{2}{7} \div 1 \)**: \[ \frac{2}{7} \div 1 = \frac{2}{7} \] 4. **Now calculate \( \frac{2}{7} - \frac{5}{3} \)**: To perform this subtraction, we need a common denominator. The least common multiple of 7 and 3 is 21. \[ \frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21} \] \[ \frac{5}{3} = \frac{5 \times 7}{3 \times 7} = \frac{35}{21} \] Now we can subtract: \[ \frac{6}{21} - \frac{35}{21} = \frac{6 - 35}{21} = \frac{-29}{21} \] 5. **Now we have \( 0 - \left( \frac{-29}{21} \right) \div ( \frac{2}{7}, 1 ) \)**. The expression \( ( \frac{2}{7}, 1 ) \) is not clear, but if we assume it means just \( \frac{2}{7} \), we can proceed with that. 6. **Calculate \( \frac{-29}{21} \div \frac{2}{7} \)**: Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{-29}{21} \div \frac{2}{7} = \frac{-29}{21} \times \frac{7}{2} = \frac{-29 \times 7}{21 \times 2} = \frac{-203}{42} \] 7. **Now we have \( 0 - \frac{-203}{42} \)**: \[ 0 - \frac{-203}{42} = \frac{203}{42} \] Thus, the final result is \[ \boxed{\frac{203}{42}} \]