To solve the expression:

$-\frac{3}{5} + \frac{6}{7} + \left(-\frac{2}{35}\right)$

1. Find a common denominator for all three fractions. The denominators are 5, 7, and 35. The least common denominator (LCD) is 35.

2. Rewrite each fraction with the LCD of 35:

   • $-\frac{3}{5} = -\frac{21}{35}$ (since $3 \times 7 = 21$)
   • $\frac{6}{7} = \frac{30}{35}$ (since $6 \times 5 = 30$)
   • $-\frac{2}{35}$ remains $-\frac{2}{35}$

3. Add the fractions:

$-\frac{21}{35} + \frac{30}{35} - \frac{2}{35} = \frac{-21 + 30 - 2}{35} = \frac{7}{35}$

4. Simplify $\frac{7}{35}$:

$\frac{7}{35} = \frac{1}{5}$

So, the final answer is:

$\boxed{\frac{1}{5}}$

Would you like further details or have any questions?

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Here are 5 related questions:

1. How do you find the least common denominator for multiple fractions?
2. Can you simplify $\frac{-2}{7} + \frac{3}{14}$?
3. How do you subtract fractions with different denominators?
4. What is the result of $\frac{5}{6} + \frac{-7}{8}$?
5. How can mixed numbers be added or subtracted?

Tip: When adding or subtracting fractions, always ensure they have a common denominator before performing the operation.