Algebra - Algebraic Expressions

Simplify: $\;$ $\dfrac{2b + a - \dfrac{4a^2 - b^2}{a}}{b^3 + 2ab^2 - 3a^2 b} \times \dfrac{a^3 b - 2a^2 b^2 + ab^3}{a^2 - b^2}$


$\dfrac{2b + a - \dfrac{4a^2 - b^2}{a}}{b^3 + 2ab^2 - 3a^2 b} \times \dfrac{a^3 b - 2a^2 b^2 + ab^3}{a^2 - b^2}$

$= \dfrac{2ab + a^2 - 4a^2 + b^2}{ab \left(b^2 + 2ab - 3a^2\right)} \times \dfrac{ab \left(a^2 - 2ab + b^2\right)}{\left(a + b\right) \left(a - b\right)}$

$= \dfrac{2ab - 3a^2 + b^2}{b^2 + 2ab - 3a^2} \times \dfrac{\left(a - b\right)^2}{\left(a + b\right) \left(a - b\right)}$

$= \dfrac{a - b}{a + b}$