Perform the indicated operations and simplify the expression.

$$\frac{1}{2}x^{-1/4}=\frac{1}{2x^{0.25}}=\frac{1}{2\sqrt[4]{x}}$$

Perform the indicated operations and simplify the expression.

$$\small{\text{ $ \left( x^{\frac{1}{4}} + 1 \right) \cdot \textcolor[rgb]{1,0,0}{\left( \dfrac{1}{4}x^{-\frac{1}{4}} \right)} - \left( x^{\frac{1}{4}} - 1 \right) \cdot \textcolor[rgb]{1,0,0}{\left( \dfrac{1}{4}x^{-\frac{1}{4}} \right)} $}}\\ \small{\text{ $ = \textcolor[rgb]{1,0,0}{\left( \dfrac{1}{4}x^{-\frac{1}{4}} \right)} \cdot \left[ \left( x^{\frac{1}{4}} + 1 \right) - \left( x^{\frac{1}{4}} - 1 \right) \right] $}}\\\\ \small{\text{ $ = \left( \dfrac{1}{4}x^{-\frac{1}{4}} \right) \cdot \left( \not{x^{\frac{1}{4}}} + 1 - \not{x^{\frac{1}{4}}} + 1 \right) $}}\\\\ \small{\text{ $ =\left( \dfrac{2}{4}x^{-\frac{1}{4}} \right) $}}\\\\ \small{\text{ $ =\left( \dfrac{1}{2}x^{-\frac{1}{4}} \right) $}}$$