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$((\sqrt[4]{a}-\sqrt[4]{b})^{-2}+(\sqrt[4]{a}+\sqrt[4]{b})^{-2}):\frac{a^{\frac{1}{2}}+b^{\frac{1}{2}}}{a-b}=\\\\(\frac{1}{(\sqrt[4]{a}-\sqrt[4]{b})^2}+\frac{1}{(\sqrt[4]{a}+\sqrt[4]{b})^2})(\sqrt{a}-\sqrt{b})=\frac{\sqrt{a}-\sqrt{b}}{(\sqrt[4]{a}-\sqrt[4]{b})^2}+\frac{\sqrt{a}-\sqrt{b}}{(\sqrt[4]{a}+\sqrt[4]{b})^2}=\\\\$ $\frac{(\sqrt[4]{a}-\sqrt[4]{b})(\sqrt[4]{a}+\sqrt[4]{b})}{(\sqrt[4]{a}-\sqrt[4]{b})^2}+\frac{(\sqrt[4]{a}-\sqrt[4]{b})(\sqrt[4]{a}+\sqrt[4]{b})}{(\sqrt[4]{a}+\sqrt[4]{b})^2}=\frac{\sqrt[4]{a}+\sqrt[4]{b}}{\sqrt[4]{a}-\sqrt[4]{b}}+\frac{\sqrt[4]{a}-\sqrt[4]{b}}{\sqrt[4]{a}+\sqrt[4]{b}}=\\\\$ $\frac{(\sqrt[4]{a}+\sqrt[4]{b})^2+(\sqrt[4]{a}-\sqrt[4]{b})^2}{(\sqrt[4]{a}-\sqrt[4]{b})(\sqrt[4]{a}+\sqrt[4]{b})}=2*\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}$