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