(3/7+3/5):9/7=

To solve the expression \((3/7 + 3/5) : (9/7)\), we can follow these steps: 1. **Add the fractions in the numerator**: \[ \frac{3}{7} + \frac{3}{5} \] To add these fractions, we need a common denominator. The least common multiple of 7 and 5 is 35. Convert both fractions: \[ \frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35} \] \[ \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35} \] Now, add the two: \[ \frac{15}{35} + \frac{21}{35} = \frac{15 + 21}{35} = \frac{36}{35} \] 2. **Now, substitute back into the expression**: \[ \frac{36}{35} : \frac{9}{7} \] 3. **Convert the division of fractions**: Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{36}{35} \div \frac{9}{7} = \frac{36}{35} \times \frac{7}{9} \] 4. **Multiply the fractions**: \[ \frac{36 \times 7}{35 \times 9} = \frac{252}{315} \] 5. **Simplify the fraction**: Find the greatest common divisor (GCD) of 252 and 315, which is 63: \[ \frac{252 \div 63}{315 \div 63} = \frac{4}{5} \] Thus, the final result of the expression \((3/7 + 3/5) : (9/7)\) is: \[ \boxed{\frac{4}{5}} \]