How can I understand solving the equation? $$\begin{align}
&\left[(\sqrt[4]{p}-\sqrt[4]{q})^{-2} + (\sqrt[4]{p}+\sqrt[4]{q})^{-2}\right] : \frac{\sqrt{p} + \sqrt{q}}{p-q} \\
&= \left(\frac{1}{(\sqrt[4]{p}-\sqrt[4]{q})^{2}}+\frac{1}{(\sqrt[4]{p}+\sqrt[4]{q})^{2}}\right) \times \frac{(\sqrt{p} - \sqrt{q})(\sqrt{p} + \sqrt{q})}{\sqrt{p} + \sqrt{q}} \\
&= \frac{(\sqrt[4]{p}+\sqrt[4]{q})^{2} + (\sqrt[4]{p} - \sqrt[4]{q})^{2}}{(\sqrt{p} - \sqrt{q})^{2}} \times \frac{(\sqrt{p} - \sqrt{q})(\sqrt{p} + \sqrt{q})}{(\sqrt{p} + \sqrt{q})}\end{align}$$
How can I get this expression? $$\frac{(\sqrt[4]{p}+\sqrt[4]{q})^{2} + (\sqrt[4]{p} - \sqrt[4]{q})^{2}}{(\sqrt{p} - \sqrt{q})^{2}}$$
Only this solving I can't understand.

$$(A+B)^2+(A-B)^2=(A^2+2AB+B^2)+(A^2-2AB+B^2)=2(A^2+B^2)$$ By using this identity, You can simplify the numerator. $$\dfrac{(\sqrt[4]{p}+\sqrt[4]{q})^{2} + (\sqrt[4]{p} - \sqrt[4]{q})^{2}}{(\sqrt{p} - \sqrt{q})^{2}}=\dfrac{2(\sqrt{p}+\sqrt{q})}{(\sqrt{p} - \sqrt{q})^{2}}$$ Rest will be obvious. Good luck.
