Let's solve each of the expressions one by one.

### a) \( \frac{3}{7} - \frac{5}{2} + \frac{3}{-5} \)

1. Convert all fractions to a common denominator, which is 70:
\[
\frac{3}{7} = \frac{30}{70}, \quad \frac{5}{2} = \frac{175}{70}, \quad \frac{3}{-5} = \frac{-42}{70}
\]
2. Now substitute into the equation:
\[
\frac{30}{70} - \frac{175}{70} - \frac{42}{70}
\]
3. Combine the numerators:
\[
\frac{30 - 175 - 42}{70} = \frac{30 - 217}{70} = \frac{-187}{70}
\]
4. Simplifying \( -187/70 \) would give us:
\[
- \frac{187}{70} \text{ (already in simplest form)}
\]

### b) \( \frac{1}{15} + \frac{9}{10} + \frac{14}{15} - \frac{1}{9} - \frac{1}{20} \)

1. The common denominator for all fractions here would be 180.
2. Converting:
\[
\frac{1}{15} = \frac{12}{180}, \quad \frac{9}{10} = \frac{162}{180}, \quad \frac{14}{15} = \frac{168}{180}, \quad \frac{1}{9} = \frac{20}{180}, \quad \frac{1}{20} = \frac{9}{180}
\]
3. Now substitute into the equation:
\[
\frac{12}{180} + \frac{162}{180} + \frac{168}{180} - \frac{20}{180} - \frac{9}{180}
\]
4. Combine the numerators:
\[
\frac{12 + 162 + 168 - 20 - 9}{180} = \frac{313}{180}
\]
5. \( \frac{313}{180} \) is already in simplest form.

### c) \( \frac{4}{7} - \left( \frac{1}{2} - \left( \frac{3}{7} + 2 \frac{1}{2} \right) \right) \)

1. Simplify \( 2 \frac{1}{2} \) to \( \frac{5}{2} \):
\[
\frac{3}{7} + \frac{5}{2}
\]
2. Convert to a common denominator (the common denominator is 14):
\[
\frac{3}{7} = \frac{6}{14}, \quad \frac{5}{2} = \frac{35}{14}
\]
3. Combine the fractions:
\[
\frac{6 + 35}{14} = \frac{41}{14}
\]
4. Substitute back into the whole expression:
\[
\frac{1}{2} - \frac{41}{14}
\]
5. Convert \( \frac{1}{2} \) to have the same denominator:
\[
\frac{1}{2} = \frac{7}{14}
\]
6. Combine:
\[
\frac{7}{14} - \frac{41}{14} = \frac{-34}{14} = \frac{-17}{7}
\]
7. Now substitute into the final expression:
\[
\frac{4}{7} - \frac{-17}{7} = \frac{4}{7} + \frac{17}{7} = \frac{21}{7} = 3
\]

### d) \( \frac{3}{4} \cdot \frac{11}{9} - \frac{3}{9} \cdot \frac{3}{4} + \frac{3}{4} \cdot \frac{1}{9} \)

1. Calculate each term:
\[
\frac{3 \cdot 11}{4 \cdot 9} - \frac{3 \cdot 3}{9 \cdot 4} + \frac{3 \cdot 1}{4 \cdot 9}
\]
This gives:
\[
\frac{33}{36} - \frac{9}{36} + \frac{3}{36}
\]
2. Combine the terms:
\[
\frac{33 - 9 + 3}{36} = \frac{27}{36} = \frac{3}{4}
\]

### Summary of Results:
- a) \( -\frac{187}{70} \)
- b) \( \frac{313}{180} \)
- c) \( 3 \)
- d) \( \frac{3}{4} \)