Evaluate: (4x^{(1)/(4)}+1) \times (x^{(1)/(4)}-1)

Expression: $\left( 4{x}^{\frac{ 1 }{ 4 }}+1 \right) \times \left( {x}^{\frac{ 1 }{ 4 }}-1 \right)$

Simplify the expression

$4{x}^{\frac{ 1 }{ 2 }}-4{x}^{\frac{ 1 }{ 4 }}+{x}^{\frac{ 1 }{ 4 }}-1$

Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression

$4\sqrt{ x }-4{x}^{\frac{ 1 }{ 4 }}+{x}^{\frac{ 1 }{ 4 }}-1$

Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression

$4\sqrt{ x }-4\sqrt[4]{x}+{x}^{\frac{ 1 }{ 4 }}-1$

Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression

$4\sqrt{ x }-4\sqrt[4]{x}+\sqrt[4]{x}-1$

Collect like terms

$4\sqrt{ x }-3\sqrt[4]{x}-1$