(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: \[ \boxed{\frac{4}{5}} \]