To solve the expression $\frac{3}{7} - \frac{7}{9} + \frac{3}{5}$, follow these steps:

1. Find a common denominator:
   The denominators are 7, 9, and 5. The least common denominator (LCD) for these is 315.

2. Convert each fraction to have the common denominator:

   • $\frac{3}{7} = \frac{3 \times 45}{7 \times 45} = \frac{135}{315}$
   • $\frac{7}{9} = \frac{7 \times 35}{9 \times 35} = \frac{245}{315}$
   • $\frac{3}{5} = \frac{3 \times 63}{5 \times 63} = \frac{189}{315}$

3. Perform the operations: $\frac{135}{315} - \frac{245}{315} + \frac{189}{315} = \frac{135 - 245 + 189}{315} = \frac{79}{315}$

So, the final answer is $\frac{79}{315}$.

Would you like more details or have any questions about this solution?

Here are 5 related questions:

1. How do you determine if a fraction can be simplified further?
2. What is the process to find the least common denominator of multiple fractions?
3. How do you convert the fraction $\frac{79}{315}$ to a decimal?
4. How would you handle an expression with more than three fractions?
5. What is the significance of finding the least common denominator when adding or subtracting fractions?

Tip: Always double-check your calculations when finding a common denominator, especially when dealing with multiple fractions.