We will solve the expression:

\[
-\frac{3}{5} + \frac{6}{7} - \frac{2}{35}
\]

### Step 1: Find a common denominator
The denominators are 5, 7, and 35. The least common denominator (LCD) is 35.

### Step 2: Rewrite each fraction with a denominator of 35
- For \(-\frac{3}{5}\), multiply both numerator and denominator by 7:
\[
-\frac{3}{5} = -\frac{21}{35}
\]
- For \(\frac{6}{7}\), multiply both numerator and denominator by 5:
\[
\frac{6}{7} = \frac{30}{35}
\]
- \(\frac{2}{35}\) is already expressed with a denominator of 35.

### Step 3: Combine the fractions
Now we add the fractions:
\[
-\frac{21}{35} + \frac{30}{35} - \frac{2}{35} = \frac{-21 + 30 - 2}{35} = \frac{7}{35}
\]

### Step 4: Simplify the result
\[
\frac{7}{35} = \frac{1}{5}
\]

Thus, the final answer is:

\[
\boxed{\frac{1}{5}}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the least common denominator for multiple fractions?
2. What is the process to add or subtract fractions with unlike denominators?
3. Can you simplify fractions when adding them without finding a common denominator?
4. How would this method apply to algebraic fractions?
5. How does subtracting negative fractions change the procedure?

**Tip:** Always simplify the fractions at the end of your calculations to ensure the result is in its simplest form.

Learn how to solve the expression -3/5 + 6/7 - 2/35 with a step-by-step solution. This problem focuses on finding the least common denominator, combining fractions, and simplifying the result. Perfect for students in Grades 6-8.

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