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.