Simplify: $\;$ $\left[\left(\dfrac{a \sqrt{a} + b \sqrt{b}}{\sqrt{a} + \sqrt{b}} - \sqrt{ab}\right) : \left(a - b\right)\right] + \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$\left[\left(\dfrac{a \sqrt{a} + b \sqrt{b}}{\sqrt{a} + \sqrt{b}} - \sqrt{ab}\right) : \left(a - b\right)\right] + \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$= \left[\dfrac{\sqrt{a} \left(a - b\right) + \sqrt{b} \left(b - a\right)}{\sqrt{a} + \sqrt{b}} : \left(a - b\right)\right] + \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$= \left[\dfrac{\left(\sqrt{a} - \sqrt{b}\right) \left(a - b\right)}{\sqrt{a} + \sqrt{b}} \times \dfrac{1}{a - b}\right] + \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$= \dfrac{\sqrt{a} - \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$= \dfrac{\sqrt{a} + \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$= 1$