https://file.aiquickdraw.com/mathbot/file/17268239294318eauxr3k.jpg

The mathematical expression in the image can be interpreted as:

\[
\frac{2a - 3b}{a} + \frac{3a + 4b}{2a}
\]

Let's break this down and simplify it step-by-step.

### Step 1: Simplify each term separately.
- For the first term \(\frac{2a - 3b}{a}\):
  \[
  \frac{2a - 3b}{a} = \frac{2a}{a} - \frac{3b}{a} = 2 - \frac{3b}{a}
  \]
- For the second term \(\frac{3a + 4b}{2a}\):
  \[
  \frac{3a + 4b}{2a} = \frac{3a}{2a} + \frac{4b}{2a} = \frac{3}{2} + \frac{2b}{a}
  \]

### Step 2: Combine the results.
Now, combine the simplified terms:
\[
2 - \frac{3b}{a} + \frac{3}{2} + \frac{2b}{a}
\]

### Step 3: Combine like terms.
We can now combine the constants and the terms involving \(b\):
\[
\left(2 + \frac{3}{2}\right) + \left(-\frac{3b}{a} + \frac{2b}{a}\right)
\]

- Combine the constants \(2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2}\).
- Combine the terms involving \(b\): \(-\frac{3b}{a} + \frac{2b}{a} = -\frac{b}{a}\).

### Final simplified result:
\[
\frac{7}{2} - \frac{b}{a}
\]

Thus, the expression simplifies to:
\[
\boxed{\frac{7}{2} - \frac{b}{a}}
\]

Would you like more details on any of the steps or have any questions?

### 5 Questions for Further Exploration:
1. How would the expression change if the second fraction were \(\frac{4a + 5b}{2a}\) instead?
2. Can you simplify \(\frac{4a - 6b}{2a} + \frac{5a + 7b}{3a}\)?
3. What happens to the expression if \(a = 1\) and \(b = 2\)?
4. How would you handle the case where \(a = 0\) in any of these terms?
5. How can you combine fractions with different denominators in algebraic expressions?

### Tip:
When simplifying expressions involving fractions, always look for common factors in the numerator and denominator to make the calculations easier!

Simplify the expression (2a - 3b)/a + (3a + 4b)/(2a)

Learn how to simplify the algebraic expression (2a - 3b)/a + (3a + 4b)/(2a) step-by-step. This solution involves key concepts such as fraction operations, simplifying algebraic terms, and combining like terms. Ideal for students in Grades 9-10.

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