Let's simplify the given expression step by step:

The expression is:

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

### Step 1: Simplify the second fraction
Notice that the second denominator \( b - 2a \) can be factored as \( -(2a - b) \). So, we rewrite the fraction:

\[
\frac{2a - b}{b - 2a} = \frac{2a - b}{-(2a - b)} = -1
\]

### Step 2: Substitute back into the expression
Now, the expression becomes:

\[
\frac{3a + 2b}{4a - b} - (-1)
\]

### Step 3: Simplify the expression
Subtracting \(-1\) is the same as adding \(1\):

\[
\frac{3a + 2b}{4a - b} + 1
\]

So the simplified form of the expression is:

\[
\frac{3a + 2b}{4a - b} + 1
\]

This is the final simplified expression.

Do you have any questions or would you like further details?

Here are 5 related questions to explore further:
1. How would the expression change if you swapped the variables \(a\) and \(b\)?
2. What happens to the expression when \(a = b\)?
3. Can you factorize the numerator \(3a + 2b\)?
4. How would you simplify this expression if \(a = 0\)?
5. How can you express the original expression in terms of a common denominator?

**Tip:** Always look for ways to factor or simplify expressions early in the process to make algebraic manipulation easier.

Learn how to simplify the algebraic expression (3a+2b)/(4a-b) - (2a-b)/(b-2a) with a step-by-step solution. This problem covers key algebraic concepts such as fraction simplification, factoring, and arithmetic operations. Suitable for students in Grades 9-10.

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