To simplify the expression \( \frac{2x - 3}{x + 9} + \frac{3}{5} \), we need to combine the two fractions.

1. Find a common denominator. The denominators are \( x + 9 \) and \( 5 \). The common denominator is \( 5(x + 9) \).

2. Rewrite each fraction with the common denominator:

   \[
   \frac{2x - 3}{x + 9} = \frac{(2x - 3) \cdot 5}{5(x + 9)} = \frac{10x - 15}{5(x + 9)}
   \]

   \[
   \frac{3}{5} = \frac{3 \cdot (x + 9)}{5 \cdot (x + 9)} = \frac{3x + 27}{5(x + 9)}
   \]

3. Now, combine the two fractions:

   \[
   \frac{10x - 15 + 3x + 27}{5(x + 9)} = \frac{13x + 12}{5(x + 9)}
   \]

Thus, the simplified expression is:

\[
\frac{13x + 12}{5(x + 9)}
\]

Would you like any further details or have any questions about this process? Here are some related questions to consider:

1. How do you find the least common denominator of two fractions?
2. Can you provide an example of adding two fractions with different denominators?
3. What is the significance of simplifying fractions in algebra?
4. How would you solve for \( x \) if \( \frac{13x + 12}{5(x + 9)} = 0 \)?
5. What happens to the expression if \( x + 9 = 0 \)?

**Tip:** When combining fractions, always ensure you simplify where possible to make calculations easier.

Learn how to simplify the algebraic expression (2x - 3) / (x + 9) + 3 / 5 by finding a common denominator and combining fractions. This problem explores key algebraic concepts such as rational expressions and fraction addition, suitable for students in Grades 8-10.

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