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The expression you provided is:

\[
\frac{9}{6} + \left( \frac{-3}{5} \right)
\]

### Step-by-step solution:

1. **Simplify \(\frac{9}{6}\):**
   - \(\frac{9}{6}\) can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3:
   \[
   \frac{9}{6} = \frac{9 \div 3}{6 \div 3} = \frac{3}{2}
   \]

2. **Find a common denominator:**
   The fractions \(\frac{3}{2}\) and \(\frac{-3}{5}\) need a common denominator. The least common denominator (LCD) of 2 and 5 is 10.
   
   - Convert \(\frac{3}{2}\) to have a denominator of 10:
   \[
   \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}
   \]
   - Convert \(\frac{-3}{5}\) to have a denominator of 10:
   \[
   \frac{-3}{5} = \frac{-3 \times 2}{5 \times 2} = \frac{-6}{10}
   \]

3. **Add the fractions:**
   Now that both fractions have a common denominator, add them:
   \[
   \frac{15}{10} + \frac{-6}{10} = \frac{15 - 6}{10} = \frac{9}{10}
   \]

Thus, the simplified result is:
\[
\frac{9}{10}
\]

Would you like a detailed explanation of any part of the solution?

Here are 5 related questions for further practice:
1. What is the sum of \(\frac{4}{3}\) and \(\frac{-2}{5}\) in simplest form?
2. Simplify \(\frac{12}{16} + \frac{-5}{8}\).
3. How do you find the least common denominator for two fractions?
4. What is the simplified form of \(\frac{7}{10} + \frac{3}{4}\)?
5. How do you convert a mixed number to an improper fraction?

**Tip:** When adding or subtracting fractions, always ensure you work with a common denominator to make the calculation easier!

Learn how to simplify and add the fractions 9/6 and -3/5 with a detailed step-by-step solution. This problem covers key concepts such as finding a common denominator and reducing fractions to their simplest form. Suitable for students in Grades 5-7.

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