Simplify: $\;$ $\dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \left\{\dfrac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\sqrt{a} + \sqrt{b}} - \dfrac{1}{\left(ab\right)^{\frac{1}{2}}}\right\} \left(a - b\right)^{-1}$
$\dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \left\{\dfrac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\sqrt{a} + \sqrt{b}} - \dfrac{1}{\left(ab\right)^{\frac{1}{2}}}\right\} \left(a - b\right)^{-1}$
$= \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \left\{\dfrac{\left(a^{\frac{1}{2}}\right)^3 + \left(b^{\frac{1}{2}}\right)^3}{\sqrt{a} + \sqrt{b}} - \left(ab\right)^{\frac{1}{2}} \right\} \times \dfrac{1}{\left(a - b\right)}$
$= \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \left\{\dfrac{\left(\sqrt{a} + \sqrt{b}\right) \left[\left(\sqrt{a}\right)^2 - \sqrt{a} \sqrt{b} + \left(\sqrt{b}\right)^2\right]}{\sqrt{a} + \sqrt{b}} - \sqrt{ab} \right\} \times \dfrac{1}{\left(a - b\right)}$
$= \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \dfrac{a - \sqrt{ab} + b - \sqrt{ab}}{a - b}$
$= \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \dfrac{a - 2 \sqrt{ab} + b}{a - b}$
$= \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \dfrac{\left(\sqrt{a} - \sqrt{b}\right)^2}{a - b}$
$= \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \dfrac{\left(\sqrt{a} - \sqrt{b}\right)^2}{\left(\sqrt{a} + \sqrt{b}\right) \left(\sqrt{a} - \sqrt{b}\right)}$
$= \dfrac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \dfrac{\sqrt{a} - \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$= \dfrac{\sqrt{a} + \sqrt{b}}{\sqrt{a} + \sqrt{b}}$
$= 1$