https://r2.erweima.ai/mathbot/image/1725980502324sstpwzf8.jpg

The image contains a mathematical expression that looks like:

\[
\frac{3x + 6}{2x + 5} + \frac{2}{9}
\]

Let's solve this expression step by step:

### Step 1: Identify the common denominator
The least common denominator (LCD) between the two fractions \(\frac{3x + 6}{2x + 5}\) and \(\frac{2}{9}\) is the product of their individual denominators:
\[
(2x + 5) \times 9 = 9(2x + 5)
\]

### Step 2: Rewrite each fraction with the common denominator
Now we will rewrite both fractions to have the same denominator:

1. Multiply the numerator and denominator of the first fraction by 9:
   \[
   \frac{3x + 6}{2x + 5} = \frac{9(3x + 6)}{9(2x + 5)} = \frac{27x + 54}{9(2x + 5)}
   \]

2. Multiply the numerator and denominator of the second fraction by \(2x + 5\):
   \[
   \frac{2}{9} = \frac{2(2x + 5)}{9(2x + 5)} = \frac{4x + 10}{9(2x + 5)}
   \]

### Step 3: Add the numerators
Since the denominators are now the same, you can add the numerators:

\[
\frac{27x + 54}{9(2x + 5)} + \frac{4x + 10}{9(2x + 5)} = \frac{(27x + 54) + (4x + 10)}{9(2x + 5)}
\]

\[
= \frac{31x + 64}{9(2x + 5)}
\]

### Final Answer:
The simplified form of the expression is:

\[
\frac{31x + 64}{9(2x + 5)}
\]

Let me know if you'd like further clarification or detailed steps on any part.

Here are 5 related questions to practice:
1. How do you find the least common denominator (LCD) of two fractions?
2. Can you simplify the expression \(\frac{4x^2 + 6x}{3x + 2} + \frac{x}{3x + 2}\)?
3. What happens if you have fractions with different variables in the denominator?
4. How do you factor the numerator or denominator in a fraction to simplify it further?
5. What is the process for solving algebraic fractions with polynomials in the numerator and denominator?

**Tip:** Always simplify both the numerator and denominator of fractions before adding or subtracting to reduce calculation complexity!

Simplify the expression (3x + 6) / (2x + 5) + 2 / 9

This lesson explains how to simplify the expression (3x + 6) / (2x + 5) + 2 / 9 using common denominators. It covers key concepts in algebra and fraction addition, suitable for students in Grades 8-10.

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