This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 2: Factor the denominator.
The denominator is $4a^2 - b^2$. This is a difference of squares, which factors as $(2a)^2 - b^2 = (2a - b)(2a + b)$.
Step 3: Simplify the expression.
Substitute the factored forms of the numerator and denominator back into the expression:
$$ \frac{2a^2 - 3ab - 2b^2}{4a^2 - b^2} = \frac{(2a + b)(a - 2b)}{(2a - b)(2a + b)} $$
Cancel out the common factor $(2a + b)$:
$$ \frac{a - 2b}{2a - b} $$
The simplified expression is $\boxed{\frac{a - 2b}{2a - b}}$.
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