Simplify: $\;$ $\dfrac{\sqrt{ab} \left(\sqrt{a} - \sqrt{b}\right)}{\left(\sqrt[4]{b} - \sqrt[4]{a}\right)^2 \sqrt[4]{b}} - \dfrac{\sqrt[4]{16 ab} \left(a + \sqrt[4]{a^3 b} + \sqrt{ab}\right)}{\sqrt[4]{a^3} - \sqrt[4]{b^3}}$
$\dfrac{\sqrt{ab} \left(\sqrt{a} - \sqrt{b}\right)}{\left(\sqrt[4]{b} - \sqrt[4]{a}\right)^2 \sqrt[4]{b}} - \dfrac{\sqrt[4]{16 ab} \left(a + \sqrt[4]{a^3 b} + \sqrt{ab}\right)}{\sqrt[4]{a^3} - \sqrt[4]{b^3}}$
$= \dfrac{a^{\frac{1}{2}} b^{\frac{1}{4}} \left(a^{\frac{1}{2}} - b^{\frac{1}{2}}\right)}{b^{\frac{1}{2}} + a^{\frac{1}{2}} - 2 b^{\frac{1}{4}} a^{\frac{1}{4}}} - \dfrac{2 a^{\frac{1}{4}} b^{\frac{1}{4}} \left(a + a^{\frac{3}{4}} b^{\frac{1}{4}} + a^{\frac{1}{2}} b^{\frac{1}{2}}\right)}{\left(a^{\frac{1}{4}}\right)^3 - \left(b^{\frac{1}{4}}\right)^3}$
$= \dfrac{a^{\frac{1}{2}} b^{\frac{1}{4}} \left(a^{\frac{1}{2}} - b^{\frac{1}{2}}\right)}{\left(a^{\frac{1}{4}} - b^{\frac{1}{4}}\right)^2} - \dfrac{2 a^{\frac{1}{4}} b^{\frac{1}{4}} a^{\frac{1}{2}} \left(a^{\frac{1}{2}} + a^{\frac{1}{4}} b^{\frac{1}{4}} + b^{\frac{1}{2}}\right)}{\left(a^{\frac{1}{4}} - b^{\frac{1}{4}}\right) \left(a^{\frac{1}{2}} + a^{\frac{1}{4}} b^{\frac{1}{4}} + b^{\frac{1}{2}}\right)}$
$= \dfrac{a^{\frac{1}{2}} b^{\frac{1}{4}} \left(a^{\frac{1}{4}} - b^{\frac{1}{4}}\right) \left(a^{\frac{1}{4}} + b^{\frac{1}{4}}\right)}{\left(a^{\frac{1}{4}} - b^{\frac{1}{4}}\right)^2} - \dfrac{2 a^{\frac{3}{4}} b^{\frac{1}{4}}}{a^{\frac{1}{4}} - b^{\frac{1}{4}}}$
$= \dfrac{a^{\frac{1}{2}} b^{\frac{1}{4}} \left(a^{\frac{1}{4}} + b^{\frac{1}{4}}\right)}{a^{\frac{1}{4}} - b^{\frac{1}{4}}} - \dfrac{2 a^{\frac{3}{4}} b^{\frac{1}{4}}}{a^{\frac{1}{4}} - b^{\frac{1}{4}}}$
$= \dfrac{a^{\frac{3}{4}} b^{\frac{1}{4}} + a^{\frac{1}{2}} b^{\frac{1}{2}} - 2 a^{\frac{3}{4}} b^{\frac{1}{4}}}{a^{\frac{1}{4}} - b^{\frac{1}{4}}}$
$= \dfrac{a^{\frac{1}{2}} b^{\frac{1}{2}} - a^{\frac{3}{4}} b^{\frac{1}{4}}}{a^{\frac{1}{4}} - b^{\frac{1}{4}}}$
$= \dfrac{a^{\frac{1}{2}} b^{\frac{1}{4}} \left(b^{\frac{1}{4}} - a^{\frac{1}{4}}\right)}{a^{\frac{1}{4}} - b^{\frac{1}{4}}}$
$= - a^{\frac{1}{2}} b^{\frac{1}{4}}$