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.

This detailed step-by-step guide explains how to solve the expression -3/5 + 6/7 + (-2/35) by finding the least common denominator (LCD). Learn the method of rewriting fractions and simplifying the result, perfect for students in Grades 6-8.

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